Question

Find the zero of the following quadratic polynomial and verify the relationship between the zero and the coefficient (I) X2
+3x-10

Answer 1

$\sf\large\underline\star{Given:-}$

$\rm{\dashrightarrow Polynomial=x^2+3x-10}$

$\sf\large\underline\star{Verify\: that:-}$

$\rm{\dashrightarrow The\: relation\: between\:zero\:and\: coefficient}$

$\sf\large\underline\star{By\:factorisation:-}$

$\tt{\mapsto x^2 + 3x - 10 = 0}$

$\tt{\mapsto x^2 + 5x -2x - 10=0}$

$\tt{\mapsto x(x+5)-2(x+5)=0}$

$\tt{\mapsto (x+5)(x-2)=0}$

$\tt{\mapsto \therefore\:x=-5\:\:,2}$

• $\sf{Here\:\:\alpha=-5\:\:\beta=2}$

$\tt{\mapsto Sum\:of\:zero=\frac{coefficient\:of\:x}{coefficient\:of\:x^2}}$

$\tt{\mapsto \alpha+\beta=\frac{-b}{a}}$

$\tt{\mapsto \alpha+\beta=-5+2}$

$\tt{\mapsto \alpha+\beta=-3}$

$\tt{\mapsto Product\:of\:zero=\frac{constant\:term}{coefficient\:of\:x^2}}$

$\tt{\mapsto \alpha\:\beta=\frac{c}{a}}$

$\tt{\mapsto \alpha\times\:\beta=-5*2}$

$\tt{\mapsto \alpha\:\beta=-10}$

$\sf\small\underline\red{Hence,\: relation\: verified:-}$