Question

What is the answer with steps?

Answer 1

Answer:

Sum of the

$\alpha \: \: and \: \: \beta$

$\alpha + \beta = - 5 + 3 \\ \alpha + \beta = - 2 \\ \frac{ - b}{a} = \frac{ - 2}{1 } \\ therefore \: \: b = 2 \\ a = 1$

Product of

$\alpha \: \: \: \: and \: \: \beta$

$\alpha \beta = ( - 5)(3) \\ \alpha \beta = - 15 \\ \frac{c}{a} = \frac{ - 15}{1} \\ therefore \: \: c = - 15 \\ a = 1$

therefore , Required quadratic equation is

${x}^{2} + 2x + ( - 15) = 0 \\ {x}^{2} + 2x - 15 = 0$

Answer 2

Given :-

The solution set = {-5,3}

To find :-

The quardratic equation for the solution set.

Solution :-

Given solution set = {-5,3}

Let α = -5 and β = 3

We know that

The quardratic equation whose roots are α and β is x²-(α+β)+αβ = 0

Now,

The required quardratic equation is x²-(-5+3)x+(-5×3) = 0

=> x²-(-2)x+(-15) = 0

=> x²+2x-15 = 0

Answer :-

The quadratic equation whose solution set is {-5,3} is x²+2x-15 = 0

Used formulae:-

→ The quardratic equation whose roots are α and β is x²-(α+β)+αβ = 0

• α and β are the roots of the equation.