# Find the quadratic equation whose solution set is 1/2, 5

An equation which has a degree equal to 2 is known as a quadratic equation.

## Answer: The quadratic equation whose solution set is 1/2 and 5 is 2x^{2} -11x + 5 = 0.

Let's look into the stepwise solution

**Explanation:**

Roots of the quadratic equation are given to be 1/2, 5.

The general form of a quadratic equation is given as

ax^{2} + bx + c = 0, where a, b are the coefficients of x^{2} , x and c is a constant.

Since, the zeros are x = 1/2 and x = 5 therefore, the factors are (x - 1/2) and (x - 5)

Thus,

(x - 1/2)(x - 5) = 0

⇒ x^{2} - (1/2)x - 5x + 5/2 = 0

⇒ x^{2} - 11x /2 + 5/2 = 0

⇒ 2x^{2} -11x + 5 = 0

### Hence, the quadratic equation with solutions 1/2 and 5 is 2x^{2} -11x + 5 = 0.

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