Question

Find the zeroes of quadratic polynomial
${x}^{2} + 7x + 10$
and find relationship between zeroes and co efficients.
​

Answer 1

$\huge{\star{\orange{\boxed{\pink{\boxed{\underline{\mathbb{\red{ANSWER:-}}}}}}}}}$

$\longrightarrow$$\sf{x}^{2} + 7x + 10$

⠀⠀⠀

$\sf{by\:splitting\:the\:middle\:term}$

⠀⠀⠀

$\longrightarrow$$\sf{{x}^{2} + 5x + 2x + 10}$

⠀⠀⠀

$\longrightarrow$$\sf{x(x+5)+2(x+5)}$

⠀⠀

$\longrightarrow$$\sf{(x+2)(x+5)}$

⠀⠀⠀

━━━━━━━━━━━━━━━━━━

⠀⠀⠀

$\sf{x+2=0}$

$\sf{x=-2}$

⠀⠀

$\sf{x+5=0}$

$\sf{x=-5}$

⠀

━━━━━━━━━━━━━━━

⠀⠀

$\sf{Sum\:of\:zeroes=-2+(-5)}$ ⠀⠀⠀$\sf\frac{ - (coeff.of \: x)}{coeff.of {x}^{2} }$

$\sf{-2-5}$ =⠀$\sf\frac{-7}{1}$

$\sf{-7}$

⠀⠀

━━━━━━━━━━━━━━━

⠀⠀

$\sf{Product\:of\:zeroes=(-2) ×(-5)=}$

$\sf\frac{constant \: term}{coeff. \: of \: {x}^{2} }$

⠀⠀⠀

$\longrightarrow$$\sf\Large{10=10}$