In this page framing quadratic equation4 we are going to see how to construct any quadratic equation with given roots.

**Question 10:**

Construct a quadratic equation whose two roots are -21 and -1

**Solution:**

Here two roots are -21 and -1

α = -21

β = -1

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

Sum of roots (α + β) = -21 + (-1)

= -21 - 1

= -22

Product of roots (α β) = -21(-1)

= 21

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

x² - (-22) x + 21 = 0

x² + 22 x + 21 = 0

**Question 11:**

Construct a quadratic equation whose two roots are -7 and 4

**Solution:**

Here two roots are -7 and 4

α = -7

β = 4

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

Sum of roots (α + β) = -7 + 4

= -3

Product of roots (α β) = -7(4)

= -28

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

x² - (-3) x + (-28) = 0

x² + 3 x - 28 = 0

**Question 12:**

Construct a quadratic equation whose two roots are -5 and 6

**Solution:**

Here two roots are -5 and 6

α = -5

β = 6

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

Sum of roots (α + β) = -5 + 6

= 1

Product of roots (α β) = -5(6)

= -30

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

x² - (1) x + (-30) = 0

x² - x - 30 = 0