Quadratic Equations –
When an equation of the form ax²+ bx + c =0, where a, b, c are considered as real numbers and a ≠ 0, is called a quadratic equations.
Examples – (i) x²- 7x + 12 = 0 is a quadratic equations in x
1 5
(ii) x + ----- = ------, when simplified, takes the form 2x²- 5x + 2 = 0
x 2
so, the given equation is quadratic equations.
Roots of a Quadratic Equation –
A number α (alpha) is called a root of ax² + bx + c = 0, if aα² + bα + c = 0
Example.1) Show that –
(i) x = 4 is a root of the equation x²- x – 12 = 0
Ans.) L.H.S = x²- x – 12
Substituting the value of x = 4, and we get –
L.H.S = 4²- 4 – 12
= 16 – 16 = 0
So, L.H.S = R.H.S
So, x = 4 is a root of the equations x²- x – 12 (Proved)
(ii) x = 2 is not a root of the equation x²- x – 12 = 0
Ans.) L.H.S = x²- x – 12
Substituting the value of x = 2, and we get –
L.H.S = 2² - 2 – 12
= 4 – 14 = - 10
So, L.H.S ≠ R.H.S
So, x = 2 is not a root of the equations x²- x – 12 (Proved)
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