Question

if the roots of the polynomial
(p)= 3x²-3x+13m-9 are inverse to each other then find tje value of m.​

Answer 1

EXPLANATION.

Quadratic polynomial.

⇒ 3x² - 3x + 13m - 9 = 0.

One root is inverse to other.

As we know that,

Let the one root be = α.

Other root = 1/α.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ α(1/α) = 13m - 9/3.

⇒ 1 = 13m - 9/3.

⇒ 3 = 13m - 9.

⇒ 3 + 9 = 13m.

⇒ 12 = 13m.

⇒ m = 12/13.

                                                                                                                         

MORE INFORMATION.

Nature of the factors 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

Given :-

If the roots of the polynomial

(p)= 3x²-3x+13m-9 are inverse to each other

To Find :-

value of m

Solution :-

Let

$\mid \pmb{Root \; 1 = \alpha}\mid$

$\mid\pmb{Other \; root = inverse }$

Therefore

Root = 1/α

We know that

$\bf Product = \alpha \beta = \dfrac{c}{a}$

$\sf \alpha \bigg(\dfrac{1}\alpha\bigg ) = 13m -\dfrac{ 9}3.$

Cancelling α

1 = 13m - 9/3

3 = 13m - 9

3 + 9 = `13m

12 = 13m

12/13 = m