Question

quadratic equation whose roots are - 1 by 3 and 5 by 3

Answer 1

Quadratic equation
$= {x}^{2} - ( \alpha + \beta)x + \alpha \beta$
$= {x}^{2} - ( \frac{ - 1}{3} + \frac{5}{3})x + \frac{ - 1}{3} \times \frac{5}{3} \\ = {x}^{2} - \frac{4}{3}x - \frac{ 5}{3} \\ or \\ = 3 {x}^{2} - 4x - 5.$







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Answer 2

So,
Given :-- α+β = 1/3
α x β = 5/3

Solution :--
$(x { }^{2} - ( \alpha + \beta )x + ( \alpha \times \beta )$
So Equation is :--
$x {}^{2} - 1 \div 3 \times x + 5 \div 3$
3x^2-x + 5


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