Question

find the value of p for which the roots of the equation 3 x square - 2pX + 6 is equal to zero are equal​

Answer 1

EXPLANATION.

To find value of p for which the roots of equation,

3x² - 2px + 6. is equal to zero are equal.

As we know that,

D = Discriminant.

⇒ D = b² - 4ac.

Roots are real and equal : D = 0.

⇒ (-2p)² - 4(3)(6) = 0.

⇒ 4p² - 72 = 0.

⇒ 4p² = 72.

⇒ p² = 72/4.

⇒ p² = 18.

⇒ p = √18.

⇒ p = 3√2.

                                                                                                                         

MORE INFORMATION.

Nature of the factor of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 roots are imaginary and unequal or complex conjugate.

Answer 2

Answer:

Given :-

• The roots for the equation 3x² - 2px + 6 = 0.

Find out :-

• Value of p.

Solution :-

➭ 3x² - 2px + 6 = 0

We know that,

⍟︎ D = b² - 4ac ⍟︎

Substituting the formula we get,

➻ (- 2p)² - 4 × 3 × 6 = 0

➻ 4p²- 12 × 6 = 0

➻ 4p² - 72 = 0

➻ 4p² = 72

➻ p² = $\cancel{\dfrac{72}{4}}$

➻ p² = 18

➻ p = $\sqrt{18}$

➻ p = $\sqrt{2 × 3 × 3}$

➠ p = 3√2

∴ The value of p is 3√2.