Question

find the zeros and verify relationship between zeros and rhe co efficient s of 5x^-8x -4​

Answer 1

$\boxed{\red{AnswEr:-}}$

➟ Zeroes are 2 and ( - 2/5).

★ GivEn :-

• The quadratic equation,

$5 {x}^{2} - 8x - 4 = 0$

• Co-efficient of $\{x}^{2}$ = 5
• Co-efficient of x = ( - 8)
• Constant = ( - 4)

★ To FinD :-

• The zeroes of the equation.
• Relationship between zeroes and the co-efficient.

★ SolutiOn :-

➟

$5 {x}^{2} - 8x - 4 = 0 \\ \\ = > 5 {x}^{2} - (10 - 2)x - 4 = 0 \\ \\ = > 5 {x}^{2} - 10x + 2x - 4 = 0 \\ \\ = > 5x(x - 2) + 2(x - 2) = 0 \\ \\ = > (x - 2)(5x + 2) = 0 \\ \\ = > (x - 2) = 0 \\ = > x = 2 \\ \\ or \: \: (5x + 2) = 0 \\ = > 5x = - 2 \\ = > x = \frac{ - 2}{5}$

➟ $\therefore$ The zeroes of Quadratic equation = 2 and -2/5

➟ Verification between zeroes and co-efficients :-

■ Sums of zeroes =

$2 + ( - \frac{2}{5} ) \\ \\ = \frac{10 - 2}{5} \\ \\ = \frac{8}{5} \\ \\ = - ( \frac{ -8}{5} ) \\ \\ = - \frac{b}{a}$

■ Products of zeroes =

$2 \times ( - \frac{2}{5} ) \\ \\ = ( - \frac{4}{5} ) \\ \\ = ( \frac{ - 4}{5} ) \\ \\ = \frac{c}{a}$