Question

Find the zeros of the polynomial y square + 4 root 3 y - 15 and wife relationship between zeros and coefficients of the polynomials

Answer 1

Here is your answer,

$y^{2}+4 \sqrt{3}y-15$

$y^{2}+5 \sqrt{3}y- \sqrt{3}y-15$

$y(y+5 \sqrt{3} )- \sqrt{3}(y+5 \sqrt{3} )$

$(y- \sqrt{3} ) (y+5 \sqrt{3} )$

[tex]y = \sqrt{3} , -5 \sqrt{3} [/tex]

Therefore zeros are $\sqrt{3} and -5 \sqrt{3}$

Verification

$\alpha + \beta =-b/a$

$-5 \sqrt{3}+ \sqrt{3} = -4 \sqrt{3}$

$-4 \sqrt{3} = -4 \sqrt{3}$

LHS = RHS

PROVED

[tex] \alpha \beta =c/a [/tex]

$-5 \sqrt{3}* \sqrt{3}= -15$

$-15 = -15$

LHS = RHS 

PROVED.....

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