Question

if the sum of roots of ax²-5x+11=0is 15 then find A​

Answer 1

Answer :

a = ⅓

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 0.

Solution :

Here ,

The given quadratic equation is ;

ax² - 5x + 11 = 0

Now ,

Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we get ;

a = a

b = -5

c = 11

Also ,

It is given that , the sum of the roots of the given quadratic equation is 15 .

=> Sum of roots = 15

=> -b/a = 15

=> -(-5)/a = 15

=> 5/a = 15

=> 5/15 = a

=> ⅓ = a

=> a = ⅓

Hence , a = ⅓ .

Answer 2

$\tt \: the \: \: \: given \: \: \: quadratic \: \: \: equation \: \: \\ \longmapsto \tt \: a {x}^{2} - 5x + 11 = 0 \\ \\ \longmapsto \tt \: the \: general \: \: \: quadratic \: \: \: equation \: \: \: \\ \\ \longmapsto \tt \: a {x}^{2} + bx + c = 0 \\ we \: get \\ \longmapsto \tt \: a = a \\ \longmapsto \tt \: b = - 5 \\ \longmapsto \tt \: c = 11 \\ \\ sum \: of \: root = 15 \\ \longmapsto \tt - b \div a = 15 \\ \\ \longmapsto \tt - (5) \div a = 15 \\ \\ \longmapsto \tt5 \div a = 15 \\ \\ \longmapsto \tt5 \div 15 = a \\ \\ \longmapsto \tt \: \frac{1}{3} = a \\ \\ \longmapsto \tt \: a = \frac{1}{3}$