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Maths-

General

Easy

Question

In the quadratic equation shown, b is constant. For what values of b does the equation have only 1 solution?
$x to the power of 2 end exponent plus b x plus 16 equals 0$

-4 only
-8 only
-4 & 4
-8 & 8

The correct answer is: -8 & 8

For a quadratic equation with only one solution, the value of its discriminant = 0 i.e. b²- 4ac = 0
Step-by-step solution:-
Comparing the given quadratic equation with the general form i.e. $a x to the power of 2 end exponent plus b x plus c equals 0$ , we get-
a = 1, b = b, c = 16
We know that for a quadratic equation with 1 solution,
$b to the power of 2 end exponent minus 4 a c equals 0$
$therefore left parenthesis b right parenthesis to the power of 2 end exponent minus 4 left parenthesis 1 right parenthesis left parenthesis 16 right parenthesis equals 0$
$therefore b to the power of 2 end exponent minus 64 equals 0$
$therefore b to the power of 2 end exponent equals 64$
∴ b = $plus divided by negative 8$ _____________ (Taking square roots both the sides)
Final Answer:-
Option D i.e. -8 & 8 is the correct Option.

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Maths-General

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