Question

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

Solution

Correct option is

b2 – 4ac ≤ 0

                           

It will have the same sign as of a if the other factor is + ive. This means that  or b2 – 4ac ≤ 0 i.e. the equation has either equal roots or imaginary roots.

SIMILAR QUESTIONS

Q1

If one root of the equation (a2 – 5a + 3)x2 + (3a – 1)x + 2 = 0 be double the other, then the value of α is:

Q2

For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

Q3

If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

Q4

If b > a, then the equation (x – a) (x – b) – 1 = 0, has

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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