Question

Form a quadratic equation whose roots are

1/3

and 5/2

​

Answer 1

k{x²-(sum of zeroes)x+ product of zeroes}

k{x²-(1/3+5/2)x+(1/3*5/2)}

k{x²-17x/6+5/6}

k=6

=> 6x²-17x+5

so the equation is 6x²-17x+5

Answer 2

Given,

The roots of a quadratic equation are given as  1/3 and 5/2.

To find,

Find the quadratic equation.

Solution,

The quadratic equation is generally represented in the form of ax²+bx+c.

We can find the quadratic equation if we know the roots of the equation by using the formula:

kx²-(Sum of roots)x+(Product of Roots).

Putting the value of roots given in the above formula.

⇒   kx²-(1/3 + 5/2)x +(1/3 × 5/2)=0.

⇒   k(x²-((2+15) / 6)x +(5/6)=0.

⇒   k(x² - (17x)/6 +5/6=0.

⇒   6x²-17x+5=0.

Hence, the quadratic equations whose roots are 1/3 and 5/2, are given as 6x²-17x+5=0.