Question

Find the value of K so that quadratic equation 3x2 - kx + 38 = 0 has equal roots., (Read as x square)

Answer 1

Value of k is ± 21.354, rounded upto 3 decimal places.

Given:

• A quadratic equation.
• $3 {x}^{2} - kx + 38 = 0$

To find:

• Find value of k, if equation has equal roots.

Solution:

Concept/Formula to be used:

A standard quadratic equation;

$\bf a {x}^{2} + bx + c = 0,where \: a \neq0$

having equal roots if it's discriminate (D)=0 i.e.$\bf {b}^{2} - 4ac = 0$

Step 1:

Write the coefficients of the equation.

On comparing the given equation with standard quadratic equation,

$a = 3 \\ b = - k \\ c = 38$

Step 2:

Put the values in the given condition.

$( { - k)}^{2} - 4(3)(38) = 0$

or

${k}^{2} - 456 = 0$

or

${k}^{2} = 456$

or

$k = \pm \sqrt{456}$

or

$\bf \red{k = \pm \: 21.354}$

Thus,

Value of k is ±21.354; rounded upto 3 decimal places.

#SPJ3

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2

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