Question

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For what value of k does the quadratic equation ${\pmb{\sf{x^2 - 4kx + 4k = 0}}}$ have equal positive integer solution!?

Options: 1 , 0 , -1 or ½

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Answer 1

Step-by-step explanation:

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Answer 2

EXPLANATION.

Quadratic equation.

x² - 4kx + 4k = 0 have equal and positive.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

For real and equal roots : D = 0.

⇒ b² - 4ac = 0.

⇒ (-4k)² - 4(1)(4k) = 0.

⇒ 16k² - 16k = 0.

⇒ 16k(k - 1) = 0.

⇒ k = 1 and k = 0.

                                                                                                                       

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.