what does cubic polynomial means?
the product of zeros are 3, -1 and -3, respectively, find cubic polynomial.
class 10th cbse rd Sharma polynomials
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2. Find a cubic polynomial with the sum, the sum of the product of its zeroes taken two at a time, and the product of its zeros as 3, -1 and -3, respectively.
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Solution:
Generally,
A cubic polynomial, say, f(x), is of the form ax3 + bx2 + cx + d.
And, can be shown w.r.t its relationship between roots as.
⇒ f(x) = k [x3 – (sum of roots)x2 + (sum of products of roots taken two at a time)x – (product of roots)]
Where k is any non-zero real number.
Here,
f(x) = k [x3 – (3)x2 + (-1)x – (-3)]
∴ f(x) = k [x3 – 3x2 – x + 3)]
Where k is any non-zero real number.