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Class ten maths Polynomial NCERT Solutions
Chapter 2: Polynomial NCERT Solutions
TEXTBOOK’S EXERCISE – 2.2
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Sol. We know that a quadratic polynomial with zeroes α and β is given by
∴ A required quadratic polynomial is
∴ A required quadratic polynomial is
∴ A required quadratic polynomial is x2+ √5.
∴ A required quadratic polynomial is x2 – x + 1.
∴ A required quadratic polynomial is
∴ A required quadratic polynomial is x2 – 4x + 1
TEXTBOOK’S EXERCISE – 2.3
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
- P(x) = x3– 3x2 + 5x -3
g(x) = x2-2
- P(x) =x4– 3x2 + 4x -3
g(x) = x2+1-x
- P(x) = x4– 5x +6
g(x) = 2 – x2
∴ By division algorithm,
x3– 3x2 + 5x -3= (x-3)(x2-2)+(7x-9)
Here, quotient = x – 3 and remainder = 7x – 9
By division algorithm,
By division algorithm,
x4 – 5x2 + 6 = (–x2 – 2)(–x2 + 2) + (–5x + 10)
Here, quotient = − x2 −2
and remainder = – 5x + 10
2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :
Since, remainder is zero, therefore
t2 – 3 is factor of 2t4 + 3t3 – 2t2 – 9t – 12.
Since, remainder is 0, therefore, x2 + 3x + 1 is a factor of 3x4 + 5x3 – 7x2 + 2x + 2
Since, remainder is not zero, therefore, x3 – 3x + 1 is not a factor of x5 – 4x3 + x2 + 3x + 1.
3. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are
Sol. Since two zeroes are
factors of the given polynomial.
is a factor of the given polynomial. Now, let us divide the given polynomial by
No, factorizing
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