Question

The value of k, so that 16x ^ 2 + kx + 1 = 0 has equal roots 1) 48 2)-8 3) 18 4) 14​ (only Brainly

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Answer 1

Quadratic Equations

A quadratic equation in a variable $x$ is an equation which is of the form $ax^2 + bx + c = 0$ where constants $a$, $b$ and $c$ are all real numbers and $a \neq 0$.

In case of a quadratic equation $ax^2 + bx + c = 0$ the expression $b^2 - 4ac$ is called the discriminant.

Step-by-step explanation:

We've been given a quadratic equation which has equal roots and we're asked to find the value of k.

The equation $16x^2 + kx + 1 = 0$ where;

• a = co-efficient of x² = 16
• b = co-efficient of x = k
• c = constant term = 1

In-order to find the value of 'k', first we should find the value of discriminate after that we can easily find the value of 'k'.

For quadratic equation $16x^2 + kx + 1 = 0$, the discriminate is;

$\implies D = \sqrt{{b}^{2} - 4ac}$

$\implies D= \sqrt{{k}^{2} - 4(16)(1)}$

$\implies D= \sqrt{{k}^{2} - 64}$

As it is given that, the quadratic equation has equal roots. Therefore, for equal roots the discriminant must be equal to zero.

$\implies \sqrt{{k}^{2} - 64} = 0$

On squaring both sides, we obtain:

$\implies \big(\sqrt{{k}^{2} - 64}\big)^2 = (0)^2$

$\implies k^2 - 64 = 0$

$\implies k^2 = 64$

$\implies k = \pm\sqrt{64}$

$\implies \boxed{k = 8, -8}$

Hence, the required value of k is -8. So, option (2) is correct.

$\rule{300}{2}$

Extra Information:

The nature of the roots of a quadratic equation is given by its discriminant (D).‎‎

Let us consider a quadratic equation $ax^2 + bx + c = 0$, then nature of roots of quadratic equation depends upon Discriminant $D = b^2 - 4ac$ of the quadratic equation.

If $D = b^2 - 4ac > 0$, then roots of the equation are real and unequal.

If $D = b^2 - 4ac = 0$, then roots of the equation are real and equal.

If $D = b^2 - 4ac < 0$, then roots of the equation are unreal or complex or imaginary.

Answer 2

Answer:

Step-by-step explanation:

answer is option b (-8 )

by using the discriminant formula  $b^{2} -4ac$

a=16, b=k,c=1

k²-4×16×1

k²=64

k=±8

if we substitute +8 it will not satisfy

if we substitute -8 it will satisfy