What is the value (s) of k for which the equation kx^2 - kx + 1 = 0 has equal roots?
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106
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.
Answered by
40
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.
- 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.
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