Question

find the quadratic equation whose roots are 2√3-5,-2√3-5
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Answer 1

ANSWER:

• Polynomial is (x²+10x+13)

GIVEN:

• α = 2√3-5
• β = -2√3-5

TO FIND:

• Quadratic equation.

SILUTION:

Quadratic polynomial :

When roots are given:

$x {}^{2} - ( \alpha + \beta \: )x + \alpha \beta .....(i)$

Here :

α = 2√3-5

β = -2√3-5

=> (α +β ) = 2√3-5+(-2√3-5)

=>(α +β) = (2√3-2√3)+(-5-5)

=>(α +β) = (-10)

=>αβ = (2√3-5)(-2√3-5)

=>αβ = (-5+2√3)(-5-2√3)

=>αβ = (-5)² -(2√3)²

=>αβ = 25 -12

=>αβ = 13

Now putting the values in eq(i)

P(x) = x²-(-10)x +13

p(x) = x²+10x+13

• Polynomial is (x²+10x+13)

Answer 2

equation is x²+10x+13=0