Question

construct quadratic equation whose one root is 15​

Answer 1

We will learn the formation of the quadratic equation whose roots are given.

To form a quadratic equation, let α and β be the two roots.

Let us assume that the required equation be ax2
2
+ bx + c = 0 (a ≠ 0).

According to the problem, roots of this equation are α and β.

Therefore,

α + β = - ba
b
a
and αβ = ca
c
a
.

Now, ax2
2
+ bx + c = 0

⇒ x2
2
+ ba
b
a
x + ca
c
a
= 0 (Since, a ≠ 0)






⇒ x2
2
- (α + β)x + αβ = 0, [Since, α + β = -ba
b
a
and αβ = ca
c
a
]

⇒ x2
2
- (sum of the roots)x + product of the roots = 0

⇒ x2
2
- Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

Formula (i) is used for the formation of a quadratic equation when its roots are given.

For example suppose we are to form the quadratic equation whose roots are 5 and (-2). By formula (i) we get the required equation as

x2
2
- [5 + (-2)]x + 5 ∙ (-2) = 0

⇒ x2
2
- [3]x + (-10) = 0

⇒ x2
2
- 3x - 10 = 0