In this page framing quadratic equation3 we are going to see how to construct any quadratic equation with given roots.

**Question 7:**

Construct a quadratic equation whose two roots are 7 and -1

**Solution:**

Here two roots are 7 and -1

α = 7

β = -1

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

Sum of roots (α + β) = 7 + (-1)

= 7 - 1

= 6

Product of roots (α β) = 7(-1)

= -7

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

x² - 6 x + (-7) = 0

x² - 6 x -7 = 0

**Question 8:**

Construct a quadratic equation whose two roots are 3 and 15

**Solution:**

Here two roots are 3 and 15

α = 3

β = 15

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

Sum of roots (α + β) = 3 + 15

= 18

Product of roots (α β) = 3(15)

= -45

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

x² - 18 x + (-45) = 0

x² - 18 x - 45 = 0

**Question 9:**

Construct a quadratic equation whose two roots are -10 and -3

**Solution:**

Here two roots are -10 and -3

α = -10

β = -3

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

Sum of roots (α + β) = -10 + (-3)

= -10 - 3

= -13

Product of roots (α β) = -10(-3)

= 30

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

x² - (-13) x + 30 = 0

x² + 13 x + 30 = 0