If one root of the quadratic equation k x2-7 x-12-0 is 3 - then find the value of k-

Given: x = 3 is the root of the quadratic equation kx2 ndash;7x + 12 = 0. Thus, x = 3 satisfies the given equation. Therefore, nbsp;k(3)2 ndash; 7(3 ...

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Byju's Answer

Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

If one root o...

Question

If one root of the quadratic equation kx² –7x + 12 = 0 is 3, then find the value of k.

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Solution

Given: x = 3 is the root of the quadratic equation kx² –7x + 12 = 0.

Thus, x = 3 satisfies the given equation.

Therefore,

k(3)² – 7(3) + 12 = 0

$\Rightarrow$ 9k – 21 + 12 = 0

$\Rightarrow$ 9k – 9 = 0

$\Rightarrow$ 9k = 9

$\Rightarrow$ k = $\frac{9}{9} = 1$

Therefore, the value of k is 1.

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If one root of the quadratic equation kx2 –7x + 12 = 0 is 3, then find the value of k.

Given: x = 3 is the root of the quadratic equation kx2 –7x + 12 = 0. Thus, x = 3 satisfies the given equation. Therefore, k(3)2 – 7(3) + 12 = 0 ⇒ 9k – 21 + 12 = 0 ⇒ 9k – 9 = 0 ⇒ 9k = 9 ⇒ k = 99 = 1 Therefore, the value of k is 1.

If one root of the quadratic equation kx² –7x + 12 = 0 is 3, then find the value of k.