Question

If ax2 + bx + cabc Ïµ R has no real zeros, and if c < 0, then,

Solution

Correct option is

a < 0

Let f (x) = ax2 + bx + c. Since f (x) has no real zeros, either f (x) > 0 orf (x) < 0 for all x Ïµ R. Since f (0) = c < 0, we get f (x) < 0 ∀ x Ïµ R. therefore a < 0 as the parabola y = f (x) must open downwards.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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Q5

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Q6

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

Q7

If abc Ïµ R and a + b + c = 0, then the quadratic equation 3 ax2 + 3ax2 + 2bx + c = 0 has

Q8

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

Q9

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Q10

If x is real, then the maximum value of