Question

4. Determine whether the values given against each of the quadratic equation are the

roots of the equation.

(1) x2 + 4x - 5 = 0 , x = 1, -1​

Answer 1

Step-by-step explanation:

Given :-

x²+ 4x - 5 = 0 ,x = 1 and -1

To find :-

Determine whether the values given against each of the quadratic equation are the roots of the equation.

Solution :-

Given quardratic equation is x²+4x-5 = 0

We know that

If the given value satisfies the given equation then the value is a root or solution of the given equation. (i.e.LHS = RHS)

I) Given value x = 1

Put x = 1 in the given equation then

=> 1²+4(1)-5

=> 1+4-5

=> 5-5

=> 0

1 is the root of the given equation

ii) Given value x = +1

Put x = -1 in the given equation then

=> (-1)²+4(-1)-5

=> 1-4-5

=> 1-9

=> -8

-1 is not the root of the given equation .

Answer:-

1 is the root of the given quardratic equation.

-1 is not the root of the given quardratic equation.

Used formulae:-

• If the given value satisfies the given equation then the value is a root or solution of the given equation. (i.e.LHS = RHS)

Factor Theorem :-

• Let P(x) be q quardratic polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0.