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Find the zeroes of quadratic polynomial y2 +4 root 3y -15 ?

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$eginarrayl extQuadratic polynomial fleft(y ight)=y^2+4sqrt3y-15\ extcomparing the polynomial with standard form ay^2+by+c=0, extwe get a=1, b=4sqrt3,c=-15\ extWe can use fracleft[left(-b ight)pmsqrtleft[left(b^2 ight)-4ac ight] ight]2a ext to find zeroes.\ extputting coefficients in equationRightarrow fracleft[left(-4sqrt3 ight)pmsqrtleft[left(4sqrt3 ight)^2-4left(-15 ight) ight] ight]2 imes1Rightarrowfracleft[left(-4sqrt3 ight)pmsqrtleft[left(48+60 ight) ight] ight]2\ Rightarrowfracleft[left(-4sqrt3 ight)pmsqrt108 ight]2Rightarrowfracleft[left(-4sqrt3 ight)pm6sqrt3 ight]2\ extFirst zero=fracleft[left(-4sqrt3 ight)+6sqrt3 ight]2=frac2sqrt32=sqrt3\ extSecond zero=fracleft[left(-4sqrt3 ight)-6sqrt3 ight]2=frac10sqrt32=5sqrt3\ endarray$

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Deependra Verma

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