Question

The ratio of sum and product of the roots of the given equation is 3x^2+12-13x=0 a)12:13 b)13:12 c)6:7 d)7:6

Answer 1

Answer :

option (b) 13:12

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

• Ratio of sum and product of roots ,

(α + ß)/αß = (-b/a) / (c/a) = -b/c

Solution :

Here ,

The given quadratic equation is ;

3x² + 12 - 13x = 0 .

The given quadratic equation can be rewritten as ; 3x² - 13x + 12 = 0 .

Now ,

Comparing the above equation with the general quadratic equation ax² + bx + c = 0 ,

We have ;

a = 3

b = -13

c = 12

Thus ,

The ratio of sum and product of the roots of given quadratic equation will be -b/c

-b/c = -(-13)/12 = 13/12 .

Hence ,

Required ratio is 13:12 .

Answer 2

▪ Given -

• Ratio & sum of product of roots of given quadratic Eqn is 3x^2 + 12 - 13x = 0

▪ To Find -

• To find ratio of given Quadratic Eqn

▪ Solution -

We know the general quadratic Eqn Form i.e,

$★ {ax}^{2} + bx + c = 0$

We can write the given quadratic Eqn in it's original form of general quadratic Eqn,

$★ {3x}^{2} - 13x + 12 = 0$

Here,

• a = 3 (1st term)
• b = -13 (2nd term)
• c = 12 (3rd term)

We know that to find ratio of sum & product of roots of quadratic Eqn is,

$★ \frac{ - b}{c}$

Placing Values,

$⟹ \frac{ - ( - 13)}{12}$

$⟹ \frac{13}{12}$

⛬ Option (b) is correct!