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Answer :

The general form of cubic equation is \(ax^3 + bx^2 + cx + d\)

Let the three zeroes be p,q and r

Here:

\(p + q + r\) = \({{-b}\over{a}} = 2\) ............(i)

\(pq + qr + rp\) = \({{c}\over{a}} = -7\)..........(ii)

\(pqr\) = \({{-d}\over{a}} = -14\).................(iii)

On equating (i), (ii) and (iii) => \(a = 1,b = -2,c = -7,d = 14\)

Putting the values of a,b,c and d in general form

=> \(x^3 - 2x^2 - 7x + 14\)

- Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: (i) \(2x^3 + x^2 - 5x + 2 ; {{1}\over{2}},1,-2\) (ii) \(x^3 - 4x^2 + 5x - 2 ; 2,1,1\)
- If the zeroes of the polynomial \(x^3 - 3x^2 + x + 1\) are \(a-b , a , a+b\) find \(a\) and \(b\).
- If the two zeroes of the polynomial \(x^4- 6x^3 - 26x^2 -138x - 35\) are \(2 + \sqrt{3}\) and \(2 - \sqrt{3}\) find other zeroes.
- If the polynomial \(x^4- 6x^3 + 16x^2 -25x + 10\) is divided by another polynomial \(x^2 -2x + k \) the remainder comes out to be \(x +a\) find \(k\) and \(a\).

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