Question

9. 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 :​

Answer 1

Answer:

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.

Step-by-step explanation:

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Answer 2

Answer:

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

${x}^{2} - 5x + 5 = 0$