Question

Find the value of k for which the equation 4x^+kn+8=0 has real and equal root. whoever will answer I will mark you as brainlist plzz answer if anyone knows.​

Answer 1

$\huge\underline\mathbb{\red Q\pink{U}\purple{ES} \blue{T} \orange{IO}\green{N :}}$

Find the value of k for which the equation 4x² + kx + 8 = 0 has real and equal root.

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

★ Given equation,

↪ 4x² + kx + 8 = 0

★ To find,

• Value of k.

★ Let,

• a = 4
• b = k
• c = 8

$\tt\: By \: using \: Discrimination \: (∆) \: formula$

$\tt\blue{ ↪ b^{2} - 4ac = 0}$

• Substitute the values.

$\sf\:⟹ (k)² - 4(4)(8) = 0$

$\sf\:⟹ k² - 128 = 0$

$\sf\:⟹ k² = 0 + 128$

$\sf\:⟹ k² = 128$

$\sf\:⟹ k = \sqrt{128}$

$\sf\:⟹ k = 8\sqrt{2}$

$\underline{\boxed{\bf{\purple{∴ Hence, \: the \: value \: of \: k \: is “ \: 8\sqrt{2} \: ”}}}}$

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★ Extra information,

$\bf\: ◼ \: ∆ < 0, no \: real \: roots.$

$\bf\: ◼ \: ∆ > 0, two \: distinct \: real \: roots.$

$\bf\: ◼ \: ∆ = 0, two \: equal \: real \: roots.$

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