Question

28. Find the value of k for which the roots of the equation 3x²- 10x +k=0
are reciprocal of each other.​

Answer 1

EXPLANATION.

Roots of the equation.

3x² - 10x + k = 0. are reciprocal to each other.

As we know that,

Let one roots be = α.

Other roots is reciprocal to each other = 1/α.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ α x 1/α = k/3.

⇒ 1 = k/3.

⇒ k = 3.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, 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 :-

3x² - 10x + k

To Find :-

Value of k

Solution :-

Let the root be α

Then reciprocal of root α will be 1/α

Now

Sum of zeroes = -b/a

Product of zeroes = c/a

Here

b = -10

a = 3

c = k

α × β = c/a

α × 1/α = k/3

α/α = k/3

1 = k/3

1 × 3 = k

3 = k

Hence

Value of k is 3