Q1: Find the roots of the following quadratic equations by factorization:
(i) x2 – 3x – 10 = 0
(ii) 2x2 + x – 6 = 0
(iii) √2 x2 + 7 x + 5√2 = 0
(iv) 2x2 – x + 1/8 = 0
(v) 100 x2 – 20x + 1 = 0
Answer:
x2– 3x – 10 = 0So we can write middle term as -3x = -5x + 2x
x2– 5x + 2x – 10 = 0
x(x - 5) + 2(x - 5) = 0
(x - 5)(x + 2) = 0
x - 5 = 0 and x + 2 = 0
x = 5 and x = -2
5 and -2 are our required root of quadratic equation.
2x2 + 4x – 3x – 6 = 0
2x(x + 2) – 3(x + 2) = 0
(x + 2)(2x – 3) = 0
x + 2 = 0 and 2x – 3 = 0
x = –2 and x = 3/2
–2 and 3/2 are our required root of quadratic equation.
(iii) √2 x2 + 7x + 5√2 = 0
Similarly multiply √2 with 5√2 and we get 10
Pairs of 10 are
1*10 = 10 sum 1+ 10 = 11
So our required pair is 2 and 5
√2 x2 + 5x + 2x + 5√2 = 0
x (√2x + 5) + √2(√2x + 5) = 0
(√2x + 5)(x + √2) = 0
√2x + 5 = 0 and x + √2 = 0
x = –5/√2 and x = –√2
–5/√2 and –√2 are our required root of quadratic equation.
(iv) 2x2 – x + 1/8 = 0
Multiply by 8 we get
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