Question

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

Solution

Correct option is

– 15 < a < –2

y has to be + ive

 

 ∴ since sign of 1st term is + ive, therefore the expression will be + ive   6 P. 1218 if Δ < 0 64 (a + 5)2 + 64 (7a + 5) < 0

a2 + 17 a + 30 < 0 or (a + 15) (a + 2) < 0

or – 15 < a < – 2

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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