Question

If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 +px + q = 0 has equal roots, the value of q is

Solution

Correct option is

49/4

Since 4 is a root of x2 + px + 12 = 0, we have

        16 + 4p + 12 = 0 or p = – 7.

Further, since the roots of x2 + px + q = 0 are equal, we have

        p2 – 4q = 0   or   49 – 4q = 0.

∴               q = 49/4.

SIMILAR QUESTIONS

Q1

If the roots of the equation bx2 + cx + a = 0 be expression, then for all real values of x, the expression 3b2 x2 + 6bcx + 2c2 is

Q2

If , for all x Ïµ R, then

Q3

If x is real, the maximum value of  is:

Q4

If the roots the equation ax2 + bx + c = are real and of opposite sign then the roots of the equation α (x – β)2 + β (x – α)2 = 0 are

Q5

abc are length of sides of an scalene triangle. If equation

           

has real and distinct roots, then the value of λ is given by:

Q6

A quadratic equation with rational coefficients can have

Q7

If the roots of ax2 + bx + c = 0 are in the ratio mn then

Q8

For real x, the expression [(x + m)2 – 4mn]/[2(x – n)] can be have any value except

Q9

If the expression y2 + 2xy + 2x + my – 3 can be resolved into two rational factors, then m must be

Q10

If x2 + px + 1 is a factor of ax2 + bx + c, then