Question

the ratio of the sum and product of roots of the equation 7x square -12x +18 =0 is ? a)7:12 b)7:18 c)3:2 d)2:3​

Answer 1

Answer:

Question : -

The ratio of the sum and product of the roots of the quadratic equation 7x² - 12x + 18 = 0 is ?

a ) 7 : 12

b ) 7 : 18

c ) 3 : 2

d ) 2 : 3

Answer : -

Given : -

Quadratic equation : 7x² - 12x + 18 = 0

Required to find : -

Ratio of the sum and product of the roots ?

Conditions used : -

Here, conditions refer to the relationship between the zeroes and the coefficients of the quadratic equation .

Solution : -

Quadratic equation : 7x² - 12x + 18 = 0

We need to find the ratio of the sum and product of the roots ?

So,

Let find the roots of the equation .

The standard form of the Quadratic equation is ax² + bx + c = 0

Now,

Let's compare this standard form of the Quadratic equation with the given polynomial .

Hence,

a = 7

b = - 12

c = 18

Let's find the value of the sum of the roots and the product of the roots .

Here,

Let's consider that alpha ( α ) , beta ( β ) are the roots of the quadratic equation .

We know that ;

The relationship between the sum of the zeroes and the coefficients is ;

So,

This implies ;

➪ α + β = - b/a

➪ α + β = - ( - 12 )/7

➪ α + β = 12/7

Hence,

Value of sum of the roots = 12/7

Similarly,

The relationship between the product of the zeroes and the coefficients is ;

This implies ;

➪ α.β = c/a

➪ α.β = 18/7

Hence,

Value of product of the roots = 18/7

Now,

Let's find the ratio of the sum of the roots is to product of the roots

This implies ;

➪ α + β : α.β

➪ 12/7 : 18/7

However,

we know that ;

a : b can also be written as a/b

So,

➪ α + β : α.β

➪ 12/7 ÷ 18/7

➪ 12/7 x 7/18

➪ 12/18

➪ 12 : 18

By reducing using 6 table we get ;

➪ 2 : 3

Therefore,

The ratio of the sum and the product of the roots is 2 : 3

Hence,

Option - d is correct 

Answer 2

correct answer is 2:3

option no. (d)