Question

For what values of k, the equation 9x2+6kx+4 =0 has equal roots

Answer 1

Answer:

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Answer 2

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${\large{\bold{\sf{\underline \pink{Given \; that \: : - }}}}}$

★ The equation 9x² + 6kx + 4 = 0 has equal roots

${\large{\bold{\sf{\underline {To \; find : - }}}}}$

★ The value of k.

${\large{\bold{\sf{\underline \pink{Solution \: : - }}}}}$

★ The value of k = 2

${\large{\bold{\sf{\underline{Knowledge \; required : - }}}}}$

★ The general form of quadratic equation is ax² + bx + c = 0

★ The value of the discriminant is b² - 4ac

${\large{\bold{\sf{\underline \pink{Full \; Solution \: : - }}}}}$

~ Let us calculate discriminant..!

➝ 9x² + 6kx + 4 = 0

➝ (6k)² - 4(9)(4) = 0

➝ (36k)² = 4(36)

➝ k² = 4

➝ k = √4

➝ k = 2

Henceforth, 2 is the value of k for the equation 9x² + 6kx + 4 = 0 has equal roots.

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${\large{\bold{\sf{\underline{Extra \; knowledge : - }}}}}$

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

★ The value of the discriminant is b² - 4ac

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