Question

A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is 1 point (a) x²– 6x + 2 (b) x² – 36 (c) x²– 6 (d) x² – 3

Answer 1

Question :–

▪︎A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, then quadratic will be :

(a) x²– 6x + 2

(b) x² – 36

(c) x²– 6

(d) x² – 3

ANSWER :–

• Quadratic Polynomial is x² - 36

GIVEN :–

• One zero of quadratic Polynomial is 6.

• Sum of zeros = 0

TO FIND :–

• Quadratic Polynomial = ?

SOLUTION :–

▪︎ Let's assume a quadratic Polynomial ax² + bx + c = 0 have root 6 and β .

• According to the question –

⇒ Sum of roots = 6 + β

⇒ 0 = 6 + β

⇒ β = -6

⇨ Hence , roots are 6 and -6.

▪︎ We know that a quadratic Polynomial is x² - [sum of roots](x) + (Product of roots)

• Now put the values –

⇒ x² - (6 - 6) x + (6)(-6)

⇒ x² - (0)x - 36

⇒ x² - 36

Hence , OPTION (b) is correct .

Answer 2

Given: A polynomial having one of its zeros as 6 and the sum of the zeros being equivalent to 0.

To find: The polynomial.

Answer:

Let's assume ax² + bx + c is a polynomial, where,

• The sum of the zeros is given by -b/a.
• The product of the zeros is c/a.

As per the question, the sum of the zeros is 0.

Let's assume that the zeros are α and β.

⇒ α + β = 0

⇒ 6 + β = 0 [since one zero is 6]

⇒ β = -6

Therefore, the other zero is -6.

Now, the general form of a quadratic polynomial is:

x² - [Sum of the zeros]x + [Product of the zeros]

Using this form to create the polynomial,

x² - [6 - 6]x + [6*-6]

x² - 0x - 36

x² - 36

Therefore, the right option is (b) x² - 36.