### Eamcet - Maths - Quadratic Equations

If the quadratic equation ax2+bx+c=0 if a and c are of opposite signs and b is real,then roots of the equation are

A.  Real and distinct

B.  Real and equal

C.  imaginary

D.  Both roots positive

Real and distinct

Explanation :
No Explanation available for this question

If x4 then the value of x2-7x+12 is

A.  Zero

B.  positive

C.  negative

D.  not determined

positive

Explanation :
No Explanation available for this question

I: The equation of the line parallel to 2x+3y-5=0 and passing through the point (3, -4) is 2x+3y-13=0 II: The equation of the line perpendicular to 2x+3y-5=0 and passing through the point (3, -4) is 3x-2y- 17=0

A.  Only I is true

B.  Only II is true

C.  Both I and II are true

D.  Neither I nor II are true

Only II is true

Explanation :
No Explanation available for this question

If 4 < x < 8 then the value of 12x-x2-32 is

A.  Zero

B.  positive

C.  negative

D.  not determined

positive

Explanation :
No Explanation available for this question

I:If α,β are the roots of the equation ax2+bx+c=0 then the quadratic equation whose roots are α+β,αβ is a2x2+a(b-c)x-bc=0 II:If α,β are the roots of 9x2+6x+1=0 then the equations with the roots 1/α,1/β is x2+6x+9=0

A.  only I is true

B.  only II is true

C.  both I and II are true

D.  neither I nor II true

both I and II are true

Explanation :
No Explanation available for this question

The maximum value of a2-abx-b2x2 is

A.  5a2/4

B.  a2/2

C.  a

D.  -a

5a2/4

Explanation :
No Explanation available for this question

The value of ‘a’ such that the sum of cubes of the roots of the equation x2 – ax + (2a – 3)=0 assumes the minimum value is

A.   a = 0

B.  a = -1

C.  a = 2

D.  a = 3

a = 3

Explanation :
No Explanation available for this question

The extreme value of x2-5x+6 is

A.  1/4

B.  -1/4

C.  1/2

D.  -1/2

-1/4

Explanation :
No Explanation available for this question

If x2+4y2-8x+12=0 is satisfied by real values of x and y then y must lies between

A.  2,6

B.  2,5

C.  -1,1

D.  -2.-1

-1,1

Explanation :
No Explanation available for this question

If xy+2x-3y-k is resolvable into two linear factors then k=

A.  -1

B.  4

C.  6

D.  -5

6

Explanation :
No Explanation available for this question

The number having two digits such that it is 4 times the sum and three times the product of its two digits are

A.  8

B.  16

C.  24

D.  32

24

Explanation :
No Explanation available for this question

If x2+ky2+x-y is resolvable into two linear factors then k=

A.  -1

B.  1

C.  2

D.  0

-1

Explanation :
No Explanation available for this question

x2-2x+10 has minimum at x=

A.  2

B.  -1

C.  1

D.  -2

1

Explanation :
No Explanation available for this question

If one root of px2-14x+8=0 is 6 times the other,then p=

A.  3

B.  -3

C.  2

D.  1

3

Explanation :
No Explanation available for this question

If x≠3/2 then the value of 4x2-12x+9 is

A.  Zero

B.  positive

C.  negative

D.  not determined

positive

Explanation :
No Explanation available for this question

If A,B,C are the minimum value of x2-8x+17,2x2+4x-5,3x2-7x+1 then the ascending order of A,B,C is

A.  A,B,C

B.  B,C,A

C.  C,A,B

D.  B,A,C

B,C,A

Explanation :
No Explanation available for this question

The solution set of x2>4x-5 is

A.  (-∞,1-√2][1+√2,∞)

B.  R

C.  (-1,1/2)

D.  [-1,1/2]

R

Explanation :
No Explanation available for this question

If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=

A.  -8/9

B.  8/9

C.  4/9

D.  -4/9

-8/9

Explanation :
No Explanation available for this question

If the two equations x2-cx+d=0 and x2-ax+b=0 have a common root and the second equation has equal roots,then

A.  b+d=ac

B.  2(b+d)=ac

C.  b+d=2ac

D.  (b+d)2=a+c

2(b+d)=ac

Explanation :
No Explanation available for this question

If the system of equations x + y + z =6, x + 2y + 3z=10 has no solution then λ=

A.  2

B.  3

C.  4

D.  5

3

Explanation :
No Explanation available for this question

If b2-4ac>0,then the graph of y= ax2+bx+c

A.  Cuts x-axis in two real points

B.  Real and Equal

C.  Lies entirely above the x-axis

D.  Cannot be determined

Cuts x-axis in two real points

Explanation :
No Explanation available for this question

If ax2+bx+c=0 and bx2+cx+a=0 have a common root and a≠0 then a3+b3+c3/abc=

A.  1

B.  2

C.  3

D.  9

3

Explanation :
No Explanation available for this question

If α, β are different values of θ satisfying the equations 5 cos θ+12 sin θ=11 then the value of sin (α+β)=

A.  119/120

B.   5/12

C.  120/169

D.  12/5

120/169

Explanation :
No Explanation available for this question

The quadratic equation x2 + ax + bc = 0, x2 + bx + ca = 0 have a common root, then the quadratic equations whose roots are the remaining roots in the given equations is (where, a ≠ b)

A.   x2 + x + 1=0

B.  x2 - x + 1=0

C.  x2 +c x + ab=0

D.  x2 - c x + ab=0

x2 +c x + ab=0

Explanation :
No Explanation available for this question

If α,β are the roots of ax2+bx+c=0 then (α/β – β/α)2=

A.  b2(b2-4ac)/c2a2

B.  b2(b2-4ac)/ca3

C.  b2(b2-4ac)/a4

D.  b2(b2-4ac)/c4

b2(b2-4ac)/c2a2

Explanation :
No Explanation available for this question

α and β are the roots of the equation x2+px+p3=0,(p≠0).If the points (α,β) lies on the curve x=y2,then the roots of the given equation are

A.  4,-2

B.  4,2

C.  1,-1

D.  1,1

4,-2

Explanation :
No Explanation available for this question

If the roots of x2+bx+c=0 are two consecutive integers then b2-4c=

A.  0

B.  1

C.  2

D.  3

1

Explanation :
No Explanation available for this question

A number consists of two digits whose product is 30.If the digits are interchanged the resulting numbers will exceed the previously by 9.The number is

A.  56

B.  54

C.  38

D.  28

56

Explanation :
No Explanation available for this question

If the roots of x2-2(5+2k)x+3(7+10k)=0 are equal then k=

A.  1/2,1

B.  -1/2,1

C.  2,1/2

D.  2,-1/2

2,1/2

Explanation :
No Explanation available for this question

The quadratic equations x2 – 6xa = 0 and x2 – cx + 6 = 0 and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

A.  3

B.  2

C.  1

D.  4