Question

If the sum and the product of the roots of the quadratic equation ax square - 5x + c = 0 are both equal to 10, find the values of a and b

Answer 1

Answer:  

Step-by-step explanation:

 We know that

ax² - 5x + c = 0  

a = a,  b = -5, c = c

 Sum of the roots = α + β = (-b)/(a) = 10

=> 5/a = 10

Hence a = (1/2)

 Product of the roots = αβ = (c)/(a) = 10

=> (c)/(1/2) = 10

=> 2c = 10

Hence c = 5.

 Given b = -5

 Hope my answer helps you

 Harith

Answer 2

$\bold{Answer:}$

$a = \bold{\frac{1}{2}} \\ \\ b = \bold{5}$

$\bold{Step} - \bold{by} - \bold{step\ explanation:}$

$p(x) = ax^2 - 5x + b = 0 \ \ \ [ Taking \ c\ as \ b\ for the question] \\ \\ Let the roots be \alpha\ and \beta. \\ \\ \alpha + \beta = -\frac{-5}{a} = \frac{5}{a} = 10 \\ \\ a = \frac{5}{10} = \bold{\frac{1}{2}} \\ \\ \\ \alpha \beta = \frac{b}{a} = \frac{b}{\frac{1}{2}} = b \div \frac{1}{2} = b \times 2 = 2b = 10 \\ \\ b = 10 \div 2 = \bold{5}$

$\therefore\ Values of \ a\ and \ b\ are \ \bold{\frac{1}{2}}\ and \ \bold{5}\ respectively. \\ \\ \therefore\ p(x) = \frac{1}{2}x^2 - 5x + 5 = 0 \\ \\ \therefore\ \alpha = 5 + \sqrt{15} \ \ \ ; \ \ \ \beta = 5 - \sqrt{15}$

$Thank you. Have a nice day. :-) \\ \\ \\ \#adithyasajeevan$