Question

without solving findout the sum and products of root of the quadratic equation 7x^2-5mx+9a=0​

Answer 1

Answer:

Sum of roots = 5m/7

Product of roots = 9a/7

Step-by-step explanation:

Given a quadratic equation such that,

7x^2 - 5mx + 9a = 0

To find the sum and product of it's zereos.

We know that,

The general form of a quadratic equation is :-

• Ax^2 + Bx + C = 0

On Comparing the coefficients, we have,

• A = 7
• B = -5m
• C = 9a

Also, we know that,

Sum of roots = -B/A

=> Sum of roots = -(-5m)/7

=> Sum of roots = 5m/7

And,

Product of roots = C/A

=> Product of roots = 9a/7

Hence, the required sum and product of roots of the given quadratic equation are 5m/7 and 9a/7 respectively.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

$\star \: \: {\sf{ 7 {x}^{2} - 5mx + 9a = 0}}$

$\star \: \: {\sf{ 7 {x}^{2} - 5mx + 9a = 0}}$

compare it with,

$\star \: \: {\sf{ a{x}^{2} + bx + c = 0 }}$

Where a = 7 , b = -5m ,c = 9a

__________________________________

$\dagger \: \boxed{\sf{sum \: of \: roots = \frac{ - (coeff. \: of \: {x}) }{ coeff. \: {x}^{2} } = \frac{ - b}{a} }}$

$: \implies{\sf{ \frac{ - ( - 5m)}{7} }}$

$: \implies{\sf{ \frac{ 5m}{7} }}$

__________________________________

$\dagger \: \boxed{\sf{sum \: of \: roots = \frac{ constant\:term}{ coeff. \: {x}^{2} } = \frac{ c}{a} }}$

$: \implies{\sf{ \frac{ 9a}{7} }}$