In this page framing quadratic equation2 we are going to see how to construct any quadratic equation with given roots.

**Question 4:**

Construct a quadratic equation whose two roots are 24 and -3

**Solution:**

Here two roots are 24 and -3

α = 24

β = -3

**General form of any quadratic equation x² - (α + β) x + αβ = 0**

Sum of roots (α + β) = 24 + (-3)

= 24 - 3

= 21

Product of roots (α β) = 24(-3)

= -72

Now let us write the quadratic equation with sum and product of roots

x² - 21 x + (-72) = 0

x² - 21 x - 72 = 0

**Question 5:**

Construct a quadratic equation whose two roots are -1 and -5

**Solution:**

Here two roots are -1 and -5

α = -1

β = -5

**General form of any quadratic equation x² - (α + β) x + αβ = 0**

Sum of roots (α + β) = -1 + (-5)

= -1 - 5

= -6

Product of roots (α β) = -1(-5)

= 5

Now let us write the quadratic equation with sum and product of roots

x² - (-6) x + 5 = 0

x² + 6 x + 5 = 0

**Question 6:**

Construct a quadratic equation whose two roots are -7 and 5

**Solution:**

Here two roots are -7 and 5

α = -7

β = 5

**General form of any quadratic equation x² - (α + β) x + αβ = 0**

Sum of roots (α + β) = -7 + 5

= -2

Product of roots (α β) = -7(5)

= -35

Now let us write the quadratic equation with sum and product of roots

x² - (-2) x + (-35) = 0

x² + 2 x - 35 = 0