Question

The only solution to x^2 + bx + c = 0 is x = 5

Work out the values of b and c.

Answer 1

Answer:

b=-10

c=25

Step-by-step explanation:

if the only solution is 5 so

x^2+bx+c=(x-5)²=x²-10x+25

b=-10

c=25

Answer 2

For the given quadratic equation $x^{2} +b x + c=0$ value of 'b' = -10 and value of 'c' = 25.

What is quadratic equation?

" Quadratic equation are defined as the algebraic equation in which highest exponent of the variable is two. General form of quadratic equation  is $ax^{2} + bx + c=0$ where a≠0."

According to the question,

Given quadratic equation is,

$x^{2} +b x + c=0$             ______(1)

Solution of the given quadratic equation x = 5.

From this we have,

$x-5=0\\\\(x-5)^{2} =0$                      _____(2)

Equate equation (1) and (2)  to get the value of 'b' and 'c' ,

$x^{2} +b x + c=(x-5)^{2}$

⇒$x^{2} +b x + c= x^{2} -10 x + 25$

Compare Left hand side and right hand side we get,

b = -10

c = 25

Hence, for quadratic equation $x^{2} +b x + c=0$ value of 'b' = -10 and value of 'c' = 25.

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