Relation between the roots of a quadratic equation

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Let a and b be the roots of the equation (i),

Then x = a and x = b

Since a and b are the roots of the equations (i) and (ii), both the equations are identical.

Dividing equation (i) by 'a', we get

The equations (ii) and (iii) are identical.

Therefore their corresponding terms must be identical.

i.e., coefficient of x2 = 1

Examples:

Find the sum and product of the following quadratic equations without actually solving.

i)

Suggested answer:

Here a = 1, b = -8, c = 7

ii)

Suggested answer:

Here a = 3, b = -11, c =12

iii)

Suggested answer:

Here A = p, B = q, C = r

iv)

Suggested answer:

Here a = 5, b = -10, c =12



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