Class 10 Exam > Class 10 Questions > If x = 2 and x = 3 are zeros of the quadratic...
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If x = 2 and x = 3 are zeros of the quadratic polynomial x2 + ax + b, the values of a and b respectively are :
- a)5, 6
- b)- 5, - 6
- c)- 5, 6
- d)5, - 6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If x = 2 and x = 3 are zeros of the quadratic polynomial x2+ ax + b, t...
Zeros of the polynomials are the values which gives zero when their value is substituted in the polynomial
When x=2,
x2+ax+b =(2)2+a*2+b=0
4+2a+b=0
b=-4-2a ….1
When x=3,
(3)2+ 3a + b=0
9 + 3a + b=0
Substituting
9 + 3a - 4 - 2a =0
5 + a =0
a = -5
b = 6
When x=2,
x2+ax+b =(2)2+a*2+b=0
4+2a+b=0
b=-4-2a ….1
When x=3,
(3)2+ 3a + b=0
9 + 3a + b=0
Substituting
9 + 3a - 4 - 2a =0
5 + a =0
a = -5
b = 6
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Community Answer
If x = 2 and x = 3 are zeros of the quadratic polynomial x2+ ax + b, t...
Given Information
- Zeros of the quadratic polynomial are x = 2 and x = 3.
- Quadratic polynomial is x^2 + ax + b.
To Find
- Value of a and b respectively.
Solution
Using the zero property of the quadratic polynomial, we can say that if x = 2 is a zero of the polynomial, then (x - 2) must be a factor of the polynomial. Similarly, if x = 3 is a zero of the polynomial, then (x - 3) must be a factor of the polynomial.
So, the factored form of the quadratic polynomial is (x - 2)(x - 3).
Expanding this product, we get:
x^2 - 5x + 6 = (x - 2)(x - 3)
Comparing the coefficients of x^2, x, and the constant term on both sides, we get:
a = -5 and b = 6.
Therefore, the values of a and b respectively are -5 and 6.
Hence, option (C) is the correct answer.
- Zeros of the quadratic polynomial are x = 2 and x = 3.
- Quadratic polynomial is x^2 + ax + b.
To Find
- Value of a and b respectively.
Solution
Using the zero property of the quadratic polynomial, we can say that if x = 2 is a zero of the polynomial, then (x - 2) must be a factor of the polynomial. Similarly, if x = 3 is a zero of the polynomial, then (x - 3) must be a factor of the polynomial.
So, the factored form of the quadratic polynomial is (x - 2)(x - 3).
Expanding this product, we get:
x^2 - 5x + 6 = (x - 2)(x - 3)
Comparing the coefficients of x^2, x, and the constant term on both sides, we get:
a = -5 and b = 6.
Therefore, the values of a and b respectively are -5 and 6.
Hence, option (C) is the correct answer.
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If x = 2 and x = 3 are zeros of the quadratic polynomial x2+ ax + b, the values of a and b respectively are :a)5, 6b)- 5, - 6c)- 5, 6d)5, - 6Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If x = 2 and x = 3 are zeros of the quadratic polynomial x2+ ax + b, the values of a and b respectively are :a)5, 6b)- 5, - 6c)- 5, 6d)5, - 6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = 2 and x = 3 are zeros of the quadratic polynomial x2+ ax + b, the values of a and b respectively are :a)5, 6b)- 5, - 6c)- 5, 6d)5, - 6Correct answer is option 'C'. Can you explain this answer?.
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