Question

Find the value of k for which the roots of equation 3x^2-10x+k=0 are reciprocal to each other

Answer 1

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.