Question

find the value of k for which one root of the quadratic equation kx2-5x-12=0 is 4

Answer 1

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If one root of the equation is 4
i.e x = 4
Now put it in the equation we get
$k(4) {}^{2} - 5(4) - 12 = 0 \\ 16k - 20 - 12 = 0 \\ 16k - 32 = 0 \\ 16k = 32 \\ k = \frac{32}{16} \\ k = 2$
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Answer 2

Question:

Find the value of k for which one of the roots of the quadratic equation kx² - 5x - 12 = 0 is 4 .

Answer:

k = 2

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

kx² - 5x - 12 = 0

According to the question,

One of the roots of the given quadratic equation is 4 , thus x = 4 will satisfy the given quadratic equation.

Thus,

=> kx² - 5x - 12 = 0

=> k•4² - 5•4 - 12 = 0

=> 16k - 20 - 12 = 0

=> 16k - 32 = 0

=> 16k = 32

=> k = 32/16

=> k = 2

Hence,

The required value of k is 2 .