If the roots of the quadratic equation $3 x^{2} - 5 x + p = 0$ are real and unequal, then which one of the following is correct?

p = 25 / 12

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p < 25 / 12

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p > 25 / 12

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p \leq 25 / 12

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Solution

The correct option is D $p < 25 / 12$

Given equation is $3 x^{2} - 5 x + p = 0$
Comparing with standard quadratic equation $a x^{2} + b x + c = 0$ we have
$a = 3, b = - 5, c = p$
Discriminant of the quadratic equation ${3 x}^{2} - 5 x + p = 0$ is $D = b^{2} - 4 a c = (- 5)^{2} - 4 \cdot 3 \cdot p$
For the roots to be real and unequal , Discriminant should be greater than zero
$∴ 5^{2} - 4 \cdot 3 \cdot p > 0$
$\Rightarrow 25 > 12 p \Rightarrow \frac{25}{12} > p \Rightarrow p < \frac{25}{12}$
So option B is correct.

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Similar questions

Choose the option that contains like terms from the following terms.

$12 x, 12 a, 25 p, 25 q, x a n d 12 y .$

x^{2} + 5 x + p = 0 & 2 x^{2} + q x + 12 = 0

p + q =

(p - 12) x^{2} - 2 (p - 12) x + 2 = 0

p, q, r

p \neq q

(p - q) x^{2} + 5 (p + q) x - 2 (p - q) = 0

A

B

P (A) > 0.5, P (B) > 0.5

P (A \cap ¯ ¯¯ ¯ B) = \frac{3}{25}, P (¯ ¯¯ ¯ A \cap B) = \frac{8}{25},

P (A \cap B)

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