If one root of the quadratic equation x2-7 x-k-0 is 4- then find the value of k-

Given: x = 4 is the root of the quadratic equation x2 ndash;7x + k = 0. Thus, x = 4 satisfies the given equation. Therefore, (4)2 ndash; 7(4) + k = 0 ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

If one root o...

Question

If one root of the quadratic equation x² –7x + k = 0 is 4, then find the value of k.

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Solution

Given: x = 4 is the root of the quadratic equation x² –7x + k = 0.

Thus, x = 4 satisfies the given equation.

Therefore,

(4)² – 7(4) + k = 0

$\Rightarrow$ 16 – 28 + k = 0

$\Rightarrow$ –12 + k = 0

$\Rightarrow$ k = 12

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If one root of the quadratic equation x2 –7x + k = 0 is 4, then find the value of k.

Given: x = 4 is the root of the quadratic equation x2 –7x + k = 0. Thus, x = 4 satisfies the given equation. Therefore, (4)2 – 7(4) + k = 0 ⇒ 16 – 28 + k = 0 ⇒ –12 + k = 0 ⇒ k = 12

If one root of the quadratic equation x² –7x + k = 0 is 4, then find the value of k.

Given: x = 4 is the root of the quadratic equation x² –7x + k = 0.

Thus, x = 4 satisfies the given equation.

Therefore,

(4)² – 7(4) + k = 0

$\Rightarrow$ 16 – 28 + k = 0

$\Rightarrow$ –12 + k = 0

$\Rightarrow$ k = 12