Question

Solution

Correct option is

a2 – c2 =  ab

x2 + px + 1 is a factor of given cubic

∴    ax2 + bx + c = (x2 + px + 1) (ax + c)

The other factor is of first degree whose coefficients are chosen keeping in view the coefficient of x3 and constant term in cubic.

Comparing the coefficient of x2 and x.

ap + c = 0     ∴   p = – c/a a2 – c2 = ab

SIMILAR QUESTIONS

Q1

If , for all x Ïµ R, then

Q2

If x is real, the maximum value of is:

Q3

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

Q4

abc are length of sides of an scalene triangle. If equation has real and distinct roots, then the value of λ is given by:

Q5

A quadratic equation with rational coefficients can have

Q6

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

Q7

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

Q8

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

Q9

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

Q10

If 8, 2 are the roots of x2 + ax + β = 0 and 3, 3 are the roots of x2 + α xb = 0 then the roots of x2 + ax + b = 0 are