Find the zeros of the quadratic polynomial 5x^2+12x+7and verify the re

1.	Find the zeros of the quadratic polynomial 5x^2+12x+7and verify the relationship between the zeros and the coefficients
Answer» $\mathfrak{\large{\underline{\underline{<klux>GIVEN</klux>:-}}}}$ Quadratic eqn:- $\bold{ 5 {x}^{2} + 12x + 7}$ $\mathfrak{\large{\underline{\underline{To find:-}}}}$ ⭐Relation between their ZEROS and coefficient. $\mathfrak{\large{\underline{\underline{Solution:-}}}}$ Let a = 5 , b = 12 and c = 7 Let $\alpha$ and $\beta$ be the roots of the given quadratic equation. By USING MIDDLE splitting term, $\implies$ $\bold{5 {x}^{2} + 12x + 7}$ $\implies$ $\bold{ 5 {x}^{2} + 5x + 7x + 7= 0}$ $\implies$ $\bold{5x( x + 1) + 7(x + 1) = 0}$ $\implies$ $\bold{(5x + 7)(x + 1) = 0 }$ $\implies$ $\bold{x = \frac{ - 5}{7} or \: x = - 1 }$ Now, $\alpha = \frac{ - 5}{7}$ and $\beta = -1$ The relationship between sum of zeroes and coefficient of Quadratic polynomial is given by :- ★ $\boxed{\sf{ \alpha + \beta = \frac{ - b}{a} }}$ $\implies$ $\bold{ \frac{ - 5}{7} + 1 = \frac{ - 12}{5} }$ $\implies$ $\bold{ \frac{ - 7 - 5}{ 5} = \frac{ - 12}{5} }[/tex][tex]\implies$ $\bold{ \frac{-12}{5} = \frac{-12}{5} }$ L. H. S = R. H. S verified. Now, Relation between products of zeroes and their coefficient is given by :- ★ $\boxed{\sf{ \alpha \beta = \frac{c}{a} }}$ $\implies$ $\bold{ \frac{ - 7}{5} \times - 1 = \frac{7}{5} }$ $\implies$ $\bold{ \frac{7}{5} = \frac{7}{5} }$ L. H. S = R. H. S hence ,verified..