Question

If the zeroes of the quadratic polynomial x2+ (a+1)x +b are 2 and -3, then:

a) a= -7, b= -1

b) a=5, b= -1

c) a=0, b=-6​

Answer 1

Answer:

• a = -2
• b = -6

Step-by-step explanation:

According to the Question

It is given that ,

• Zeros of given polynomial are 2 & -3.
• Quadratic Polynomial = x²+(a+1)x + b

As we know that quadratic polynomial is formed by

= x² + (sum of zeros)x + (product of zeros)

➻ Sum of zeros = 2+(-3)

➻ Sum of zeros = -1

And,

➻ Product of zeros = 2×(-3)

➻ Product of zeros = -6

Now, comparing the given equation we get

➻ (a+1) = -1

➻ a + 1 = -1

➻ a = -2

and

➻ b = -6

• Hence, the required value of a & b are -2 & -6 respectively .

Answer 2

Answer :

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• Value of a and b for the given polynomial is -2 and -6.

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Explanation :

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Given :

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• Zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and -3.

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To Find :

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• Value of a and b?

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Solution :

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• We clearly know that, for finding a quadratic polynomial with sum of zeroes = S and product of zeroes = P, equation is given by : p(x) = x² - Sx + P, on comparing this equation with given polynomial we easily understand that (a + 1) is written in place of sum of zeroes S and b is written in place of product of zeroes P. So, we have sum of zeroes = (a + 1) and product of zeroes = b. Also, zeroes are given to us. So, firstly let's find sum of zeroes and product of zeroes of given polynomial.

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⚝ Finding sum of zeroes :

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➥ ⠀Sum of zeroes = 2 + (-3)

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➥ ⠀Sum of zeroes = 2 - 3

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➥ ⠀Sum of zeroes = -1

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⚝ Finding product of zeroes :

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➥ ⠀Product of zeroes = 2 × (-3)

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➥ ⠀Product of zeroes = -6

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• Also, we have sum of zeroes and product of zeroes = (a + 1) and b.

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Therefore,

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➥⠀ a + 1 = -1

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➥⠀ a = -1 - 1

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➥ ⠀a = -2

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Also,

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➥⠀ b = -6

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• Therefore, value of a and b for the given polynomial is -2 and -6.

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Learn more on brainly :

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❏ Questions :

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• Q.1 :

If alpha and beta are the zeroes of polynomial p(x) = x² - 7x + 10, find the quadratic polynomial with zeroes (-alpha) and (-beta).

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• Q.2 :

Find a quadratic polynomial whose sum of zeros is 9/2 and product of zeros is 2.

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• Q.3 :

Find zeroes of the quadratic polynomial 4x² - x - 5 and verify relationship between it's zeroes and coefficients.

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❏ Answers :

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• A.1 :

https://brainly.in/question/42822704

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• A.2 :

https://brainly.in/question/43027706

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• A.3 :

https://brainly.in/question/42964609

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