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Question

Form the quadratic equation from the roots given below.
(1) 0 and 4
(2) 3 and –10
(3) 12,-12
(4) 2-5,2+5

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Solution

(1) 0 and 4
Sum of roots = 0 + 4 = 4
Product of roots = 0 × 4 = 0
The general form of the quadratic equation is x2-Sum of rootsx+Product of roots=0
So, the quadratic equation obtained is x2-4x+0=0
x2-4x=0xx-4=0

(2) 3 and –10
Sum of roots = 3 + (–10) = −7
Product of roots = 3 × –10 = –30
The general form of the quadratic equation is x2-Sum of rootsx+Product of roots=0
So, the quadratic equation obtained is x2--7x+-30=0
x2+7x-30=0

(3) 12,-12
Sum of roots = 12+-12=0
Product of roots = 12×-12=-14
The general form of the quadratic equation is x2-Sum of rootsx+Product of roots=0
So, the quadratic equation obtained is x2-0x+-14=0
x2-14=0

(4) 2-5,2+5
Sum of roots = 2-5+2+5=4
Product of roots = 2-52+5=4-5=-1
The general form of the quadratic equation is x2-Sum of rootsx+Product of roots=0
So, the quadratic equation obtained is x2-4x+-1=0
x2-4x-1=0

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