Question

Solution

Correct option is

At least one root in [0, 1]

Let f (x) = ax3 + bx2 + cx. Note that f is continuous and derivable on R. also f (0) = 0 and f (1) = a + b + c = 0. By the rolle’s therem, there exists at least one α Ïµ (0, 1) such that Thus, 3ax2 + 2bx + c = 0 has at least one root in [0, 1].

SIMILAR QUESTIONS

Q1

The number of real roots of Q2

The product of real of the equation is

Q3

Sum of the non – real roots of  Q4

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

Q5

If x Ïµ R, the number of solution of = 1 is

Q6

If lmn are real, l + m ≠ 0, then the roots of the equation

(l + m)x2 – 3(l – m)x – 2 (l + m) = 0 are

Q7

The real values of a for which the sum of the squares of the roots of the equation x2 – (a – 2) x – a – 1 = 0 assume the least value is

Q8

If p and q are distinct primes and x2 – px + = 0 has distinct positive roots, then p + equals

Q9

The real values of a for which the quadratic equation 3x2 + 2 (a2 + 1) x+(a2 – 3a + 2) = 0 possesses roots opposite signs lie in

Q10

Let f (x) = ax2 + bx + cac, Ïµ R and a ≠ 0. Suppose (x) > 0 for all x Ïµ R.

Let g (x) = f (x) + f ’ (x) + f ”(x). Then