Question

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation is

1 point

A. x^2+10x+5=0

B. x^2–5x+5=0

C. x^2+5x–5=0

D. x^2–5x+10=0
who's option is correct​

Answer 1

Answer :–

Option (B) ${x}^{2} - 5x + 5 = 0$ is correct.

Given :–

• Sum of roots of a quadratic equation is 5.
• Product of the roots is also 5.

To Find :–

• Equation.

Solution :–

Given that,

It is a quadratic equation.

According to the question,

Sum of roots is 5, it means

⟹ $\alpha + \beta = 5$

And also given that the product of the roots is also 5, it means

⟹ $\alpha \times \beta = 5$

Now, we applied the quadratic equation in the roots formula,

So, the formula is,

⟹ ${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$Here, we know that,

⟹ $\alpha + \beta = 5$

⟹ $\alpha \times \beta = 5$

Now, put the values in the formula.

⟹ ${x}^{2} - (5)x + 5 = 0$

⟹ ${x}^{2} - 5x + 5 = 0$

Hence,

The required equation is ${x}^{2} - 5x + 5 = 0.$

So,

The option (B) is correct.

Answer 2

Answer:

given that

sum of roots of quadratic equation=5

and product =5

we know that,

sum of roots of quadratic equation=-b

and product =c

then,from the question,

square of x-b+c

hence,

x2-5x+5=0