Question

Find The value of K for which the quadratic equation 9x2+2kx+4=0 has equal roots.​

Answer 1

EXPLANATION.

Quadratic equation = 9x² + 2kx + 4 = 0

has equal roots.

Conditions for equal roots.

→ D = b² - 4ac = 0

→ (2k)² - 4(9)(4) = 0

→ 4k² - 144 = 0

→ k² = 144/4

→ k² = 36

→ k = ± 6.

More information.

(1) = D > 0 or [ b² - 4ac > 0 ]

Roots are real and unequal.

(2) = D < 0 or [ b² - 4ac < 0 ]

Roots are imaginary.

(3) = D = 0 or [ b² - 4ac = 0 ]

Roots are equal

Answer 2

$\huge\bf{{\color{black}{a}}{\color{maroon}{n}}{\red{s}}{\color{red}{w}}{\color{orange}{e}}{\color{gold}{r}}}$

$\small{ }$

$\bf {9x}^{2} + 2kx + 4 = 0 \\ \bf Given \: the \: quadratic \: equation \\ \bf has \: equal \: roots \\ \implies \bf {b}^{2} - 4ac = 0 \\ \implies \bf (2k)^{2} - 4(9)(4) = 0 \\ \implies \bf {(2k)}^{2} - 4(36) = 0 \\ \implies \bf {(2k)}^{2} - 144 = 0 \\ \implies \bf {4k}^{2} = 144 \\ \implies \bf k^{2} = \frac{144}{4} = 36 \\ \implies \bf k = \sqrt{36} \\ \therefore \bf k = \underline{ \underline{6}}$

$\small{ }$

$\huge\bf{{\color{maroon}{Hope}}~{\color{red}{it}}~{\orange{helps..!!}}}$