Question

If X= -4 is the solution of x²-10k + 24=0,find the value of k.​

Answer 1

$\bold{\blue{\underline{\red{G}\pink{iv}\green{en}\purple{:-}}}}$

• P(x) = x²- 10k + 24
• x + 4 = 0
• ∴ x = - 4

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$\bold{\blue{\underline{\red{Zeros}\pink{\:of\:}\green{\:the\:polynomials}\purple{:-}}}}$

• Zeros of the polynomial is the value of the variable for which when replaced in the polynomial the value for the polynomial changes to zero.

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$\bold{\blue{\underline{\red{General}\pink{\:form \:of }\green{\:polynomial}\purple{:-}}}}$

• $\bold{a_{n}x^n + a_{n-1}x^{n-1} +...... + a_{2}x^2 + a_{1}x + a_{0}}$

• Where ' $\bold{a_{n} , a_{n-1} ...... a_{1} , a_{0}}$ ' are Real numbers and 'n' is an integer .

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$\bold{\blue{\underline{\red{Q}\pink{uest}\green{ion}\purple{:-}}}}$

• To find the value of 'k'.

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$\bold{\blue{\underline{\red{S}\pink{olut}\green{ion}\purple{:-}}}}$

• P(x) = 0                             ∵ Given 'x' is a factor of P(x)

• -4²- 10k + 24 = 0
• 16 - 10k +24 = 0
• 40 - 10k = 0
• 40 = 10k
• k = $\bold{\frac{40}{10} }$

                                       $\bold{\green{\boxed{k = 4}}}$

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