  # If α and β are Zeros of Polynomial x²+6x+9, then Form a Quadratic Polynomial whose Zeros are -alpha, -beta.

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Updated on: October 17th, 2023 If α and β are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -α,-β.

Here are the steps to form a quadratic polynomial whose zeroes are -α and -β, given that α and β are zeroes of the polynomial x² + 6x + 9:

• Identify the factors of the polynomial x² + 6x + 9, which are (x + α) and (x + β).
• Change the signs of the zeroes to obtain the factors for the new polynomial: (x – (-α)) and (x – (-β)).
• Simplify the expressions: (x + α) and (x + β).
• Multiply the factors to obtain the quadratic polynomial: P(x) = (x + α)(x + β).
• Expand the product: P(x) = x² + (α + β)x + αβ.
• Substitute the values of α and β.
• Simplify the expression to obtain the final quadratic polynomial.

Table of content ## If α and β are Zeros of Polynomial x²+6x+9, then Form a Quadratic Polynomial whose Zeros are -alpha, -beta

If α and β are the zeroes of the quadratic polynomial x² + 6x + 9, then we can form a quadratic polynomial whose zeroes are -α and -β.

P(x) has zeroes α and β, then (x – α) and (x – β) are factors of P(x).

Given that the zeroes of the polynomial x² + 6x + 9 are α and β, we have the factors (x – α) and (x – β).

To find a quadratic polynomial with zeroes -α and -β, we can simply change the signs of the zeroes. Therefore, the factors for the new polynomial will be (x + α) and (x + β).

To find the quadratic polynomial, we multiply these factors:

P(x) = (x + α)(x + β)

Expanding this product:

P(x) = x² + (α + β)x + αβ

Since α and β are the zeroes of x² + 6x + 9,

α + β = -6, and

αβ = 9

Substituting these values:

P(x) = x² – 6x + 9

Therefore, the quadratic polynomial with zeroes -α and -β is x² – 6x + 9. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com