Question

find the quadratic polynomial whose zeroes are 4/5 and 3/10​

Answer 1

Solution :-

Given ,

• Roots of the quadratic polynomial = 4/5 & 3/10

We need to find ,

• Quadratic polynomial

As we know that ,

• Quadratic polynomial = x² - ( sum of roots ) x + ( product of roots )

Finding sum of roots & product of roots

• Sum of roots :-

→ 4/5 + 3/10

→ 40 + 15/50

→ 55/50

→ Sum of roots = 11/10

• Product of roots

→ 4/5 × 3/10

→ 12/50

→ Product of roots = 6/25

Now , finding the Quadratic polynomial

• Quadratic polynomial :-

⇒ x² - ( 11/10 ) x + 6/25

⇒ Quadratic polynomial :- x² - 11/10 x + 6/25

Hence , quadratic polynomial = x² - 11/10 x + 6/25

Answer 2

Answer :-

• x² - 11/10x + 6/25

Given :-

• Zeroes of a quadratic polynomial as 4/5 and 3/10.

To Find :-

• The quadratic polynomial.

Solution :-

As we know that

Formula for finding quadratic polynomial is

x² - (sum of zeroes)x + product of zeroes

Sum of zeroes :-

4/5 + 3/10

[ Take LCM ]

→ (8 + 3)/10

→ 11/10

Product of zeroes :-

4/5 × 3/10

→ 12/50

→ 6/25

Put the values in the formula :-

Quadratic polynomial -

x² - (α + β)x + (α × β)

→ x² - (11/10)x + (6/25)

→ x² - 11/10x + 6/25

Hence, the quadratic polynomial is x² - 11/10x + 6/25.