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If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b?
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If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the va...
Introduction:
To find the values of a and b in a quadratic polynomial, we need to know the zeros of the polynomial.
Given:
The zeros of the polynomial are 2/3 and -3. The polynomial is ax² + 7x + b.
Solution:
We know that the zeros of a quadratic polynomial are the roots of the equation ax² + bx + c = 0. Therefore, we can write two equations using the given zeros and the coefficients of the polynomial.
Equation 1:
When x = 2/3,
ax² + 7x + b = 0
a(2/3)² + 7(2/3) + b = 0
4a/9 + 14/3 + b = 0
4a + 42 + 9b = 0 (Multiplying both sides by 9)
Equation 2:
When x = -3,
ax² + 7x + b = 0
a(-3)² + 7(-3) + b = 0
9a - 21 + b = 0
Substituting b in equation 1:
4a + 42 + 9b = 0
4a + 42 + 9(-9a + 21) = 0 (Substituting b from equation 2)
4a + 42 - 81a + 189 = 0
-77a + 231 = 0
a = 3
Substituting a in equation 2:
9a - 21 + b = 0
27 - 21 + b = 0 (Substituting a = 3)
b = -6
Therefore, the values of a and b are 3 and -6, respectively.
Conclusion:
The quadratic polynomial with zeros 2/3 and -3 is 3x² + 7x - 6.
To find the values of a and b in a quadratic polynomial, we need to know the zeros of the polynomial.
Given:
The zeros of the polynomial are 2/3 and -3. The polynomial is ax² + 7x + b.
Solution:
We know that the zeros of a quadratic polynomial are the roots of the equation ax² + bx + c = 0. Therefore, we can write two equations using the given zeros and the coefficients of the polynomial.
Equation 1:
When x = 2/3,
ax² + 7x + b = 0
a(2/3)² + 7(2/3) + b = 0
4a/9 + 14/3 + b = 0
4a + 42 + 9b = 0 (Multiplying both sides by 9)
Equation 2:
When x = -3,
ax² + 7x + b = 0
a(-3)² + 7(-3) + b = 0
9a - 21 + b = 0
Substituting b in equation 1:
4a + 42 + 9b = 0
4a + 42 + 9(-9a + 21) = 0 (Substituting b from equation 2)
4a + 42 - 81a + 189 = 0
-77a + 231 = 0
a = 3
Substituting a in equation 2:
9a - 21 + b = 0
27 - 21 + b = 0 (Substituting a = 3)
b = -6
Therefore, the values of a and b are 3 and -6, respectively.
Conclusion:
The quadratic polynomial with zeros 2/3 and -3 is 3x² + 7x - 6.
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If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the va...
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If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b?
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If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b? 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 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b?.
If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b? 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 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2/3 and -3 are the zeros ofthe polunomial ax² 7x b then find the values of a and b?.
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