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If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).?
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If a and b are zeroes of the polynomial x2 – x – 6, then find a quadra...
Quadratic Polynomial with given zeroes
First, let's find the values of a and b from the given polynomial x^2 - x - 6 = 0.
Finding the values of a and b
Given polynomial: x^2 - x - 6 = 0
Since a and b are the zeroes of the polynomial, we have:
a + b = 1
ab = -6
Solving these equations, we find a = 3 and b = -2.
Finding the new zeroes
Now, we need to find the zeroes of the new quadratic polynomial:
New zeroes: (3a + 2b) and (2a + 3b)
Substitute the values of a and b:
New zeroes: (3(3) + 2(-2)) and (2(3) + 3(-2))
New zeroes: (9 - 4) and (6 - 6)
New zeroes: 5 and 0
Forming the new quadratic polynomial
Since the zeroes are 5 and 0, the quadratic polynomial can be written as:
(x - 5)(x - 0) = x^2 - 5x
Therefore, the quadratic polynomial with zeroes (3a + 2b) and (2a + 3b) is x^2 - 5x.
First, let's find the values of a and b from the given polynomial x^2 - x - 6 = 0.
Finding the values of a and b
Given polynomial: x^2 - x - 6 = 0
Since a and b are the zeroes of the polynomial, we have:
a + b = 1
ab = -6
Solving these equations, we find a = 3 and b = -2.
Finding the new zeroes
Now, we need to find the zeroes of the new quadratic polynomial:
New zeroes: (3a + 2b) and (2a + 3b)
Substitute the values of a and b:
New zeroes: (3(3) + 2(-2)) and (2(3) + 3(-2))
New zeroes: (9 - 4) and (6 - 6)
New zeroes: 5 and 0
Forming the new quadratic polynomial
Since the zeroes are 5 and 0, the quadratic polynomial can be written as:
(x - 5)(x - 0) = x^2 - 5x
Therefore, the quadratic polynomial with zeroes (3a + 2b) and (2a + 3b) is x^2 - 5x.
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If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).?
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If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).?.
If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).?.
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