An algebra problem by Vishnu Kadiri

Algebra Level 3

In solving a quadratic equation x 2 − a x + b = 0 { x }^{ 2 }-ax+b=0 ,
a boy copies a a wrongly and obtained the roots as 4 and 10,
another boy copies b b wrongly and obtained roots as 6 and 7.
Find a + b a+b .


The answer is 53.

Vishnu Kadiri by Vishnu Kadiri , 19, India

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2 solutions

Viki Zeta
Sep 17, 2016

Boy A copies just copies ’a’ wrongly, so his ’b’ would be correct. Let that function be p(x) Let α = 4 and β = 10 be the zeros of p(x). Then using Vietas formula, α × β = b 1 b = 4 × 10 = 40 Another boy copies ’b’ wrongly, so his ’a’ would be correct. Let that function be g(x) Let α = 6 and β = 7 be the zeros of g(x). Then using Vietas formula α + β = a 1 6 + 7 = a a = 13 ∴ a + b = 40 + 13 = 53 \text{Boy A copies just copies 'a' wrongly, so his 'b' would be correct. Let that function be p(x)}\\ \text{Let }\alpha =4\text{ and } \beta =10\text{ be the zeros of p(x). Then using Vietas formula, } \\ \alpha \times \beta = \dfrac{b}{1} \\ b = 4 \times 10 = 40 \\ \text{Another boy copies 'b' wrongly, so his 'a' would be correct. Let that function be g(x)} \\ \text{Let }\alpha = 6\text{ and }\beta = 7 \text{ be the zeros of g(x). Then using Vietas formula} \\ \alpha + \beta = \dfrac{a}{1} \\ 6 +7 = a \\ a = 13 \\ \therefore a + b = 40 + 13 = \fbox{ 53 }

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishnu Kadiri
Sep 17, 2016

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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