Question

What is the value (s) of k for which the equation kx^2 - kx + 1 = 0 has equal roots?
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Answer 1

EXPLANATION.

Quadratic equation.

⇒ kx² - kx + 1 = 0.

As we know that,

D = Discriminant Or b² - 4ac.

⇒ D = 0 For equal roots.

⇒ (-k)² - 4(k)(1) = 0.

⇒ k² - 4k = 0.

⇒ k(k - 4) = 0.

⇒ k = 0 and k = 4.

                                                                                                                       

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

$\huge\bf{Answer :}$

Given :

• kx² - kx + 1 = 0 is the equation.
• The above equation has equal roots.

To find :

• Appropriate value of k.

Explanation :

As we know that, for a quadratic equations having equal roots, the D ( discriminant ) must be 0.

And, D = b² - 4ac

⇒ ( - k )² - 4 ( k )( 1 ) = 0

⇒ k² - 4k = 0

• Taking k as common.

⇒ k ( k - 4 ) = 0

∴ k = 0 ✔️ or k = 4 ✔️

Hence, 0 and 4 are those values of k for which the given quadratic equation has equal roots.

$\huge\bf{Extra\: Information :}$

• The standard form of a quadratic equation is ax²+bx+c = 0, where a is coefficient of x², c is a constant term and b is the coefficient of x.
• Methods of finding roots of a quadratic equation includes prime factorisation method ( by splitting the middle term ), completing the square method or from the quadratic formula by finding dicriminant.