Question

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

Solution

Correct option is

Greater than – 4ab

Given c2 – 4ab < 0, i.e., c2 < 4ab              ….(1)

Given expression is

3 (bx + c)2 – c2 ≥ – c2 > – 4ab     by (1)

SIMILAR QUESTIONS

Q1

If α and β (α < β), are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then

Q2

If 1 lies between the roots of the equation 3x2 – 3 sin α x – 2 cos2 α = 0 then α lies in the interval

Q3

Let α,β be the roots of the equation x2 – px + r = 0 and  2β be the roots of the equation x2 – qx + r = 0. Then the value of r is

Q4

The number of real roots of the equation (x + 3)4 + (x + 5)4 = 16 is

Q5

All the values of m for which both the roots of the equation x2 – 2mx + m2– 1 = 0 are greater than – 2 but less than 4, lie in the interval

Q6

The expression ax2 + bx + c has the same sign as of a if

Q7

If the graph of the function y = 16x2 + 8(a + 5) x – 7a – 5 is strictly above the x – axis, then ‘a’ must satisfy the inequality

Q8

If tan A and tan B are the roots of the quadratic equation x2 – px + q = 0, then the value of sin2 (A + B) is

Q9

If x2 – 4x + log1/2 a does not have two distinct roots, then the maximum value of a

Q10

If , for all x Ïµ R, then