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If a and b are zero of quadratic
equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2
h?
equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2
h?
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If a and b are zero of quadratic equation equation polynomial (x)=x²-...
Quadratic Polynomial with New Zeros
First, let's find the quadratic polynomial with zeros a and b.
Given polynomial: P(x) = x² - 2x - 3
Using the sum and product of roots formula, we have:
Sum of roots (a + b) = 2
Product of roots (ab) = -3
Therefore, the quadratic polynomial with zeros a and b is:
P(x) = (x-a)(x-b)
P(x) = (x - a)(x - b)
Now, let's find the quadratic polynomial with new zeros a+2 and b+2h.
Quadratic Polynomial with New Zeros
New zeros: a+2 and b+2h
Let's consider the new polynomial as Q(x):
Q(x) = (x - (a+2))(x - (b+2h))
Q(x) = (x - a - 2)(x - b - 2h)
Q(x) = x² - (a + b + 2) x + 2(a + h) x - (ab + 2ah)
Substitute the values of a, b, and h from the given polynomial:
a + b = 2
ab = -3
Therefore, the new quadratic polynomial with zeros a+2 and b+2h is:
Q(x) = x² - (2 + 2) x + 2(a + h) x - (ab + 2ah)
Q(x) = x² - 4x + 2(a + h) x - (-3 + 2ah)
Q(x) = x² - 4x + 2(a + h) x + 3 - 2ah
So, the quadratic polynomial with zeros a+2 and b+2h is:
Q(x) = x² - 4x + 2(a + h) x + 3 - 2ah
First, let's find the quadratic polynomial with zeros a and b.
Given polynomial: P(x) = x² - 2x - 3
Using the sum and product of roots formula, we have:
Sum of roots (a + b) = 2
Product of roots (ab) = -3
Therefore, the quadratic polynomial with zeros a and b is:
P(x) = (x-a)(x-b)
P(x) = (x - a)(x - b)
Now, let's find the quadratic polynomial with new zeros a+2 and b+2h.
Quadratic Polynomial with New Zeros
New zeros: a+2 and b+2h
Let's consider the new polynomial as Q(x):
Q(x) = (x - (a+2))(x - (b+2h))
Q(x) = (x - a - 2)(x - b - 2h)
Q(x) = x² - (a + b + 2) x + 2(a + h) x - (ab + 2ah)
Substitute the values of a, b, and h from the given polynomial:
a + b = 2
ab = -3
Therefore, the new quadratic polynomial with zeros a+2 and b+2h is:
Q(x) = x² - (2 + 2) x + 2(a + h) x - (ab + 2ah)
Q(x) = x² - 4x + 2(a + h) x - (-3 + 2ah)
Q(x) = x² - 4x + 2(a + h) x + 3 - 2ah
So, the quadratic polynomial with zeros a+2 and b+2h is:
Q(x) = x² - 4x + 2(a + h) x + 3 - 2ah
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If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h?
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If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h?.
If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are zero of quadratic equation equation polynomial (x)=x²-2x-3then find the quadratic polynomial whose zero are a+2 and B+2h?.
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