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

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

A.  Zero

B.  positive

C.  negative

D.  not determined

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

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

A.  Zero

B.  positive

C.  negative

D.  not determined

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

The maximum value of a2-abx-b2x2 is

A.  5a2/4

B.  a2/2

C.  a

D.  -a

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

The extreme value of x2-5x+6 is

A.  1/4

B.  -1/4

C.  1/2

D.  -1/2

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

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

A.  -1

B.  4

C.  6

D.  -5

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

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

A.  -1

B.  1

C.  2

D.  0

x2-2x+10 has minimum at x=

A.  2

B.  -1

C.  1

D.  -2

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

A.  3

B.  -3

C.  2

D.  1

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

A.  Zero

B.  positive

C.  negative

D.  not determined

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

The solution set of x2>4x-5 is

A.  (-∞,1-√2][1+√2,∞)

B.  R

C.  (-1,1/2)

D.  [-1,1/2]

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

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

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

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

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

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

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

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

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

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

A.  0

B.  1

C.  2

D.  3

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

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

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