Therefore, ax2 + bx + c = a(x – α) (x – β)= ax2 – a(α + β)x + a α β]
Þ Division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
Q.13. 1. For which values of a and b , are the zeros of g(x) = x3+2x2+a, also the zeros of the polynomial f(x) =x5-x4-4x3+3x2+3x+b ? Which zeros of f(x) are not the zeros of g(x)?
(Ans. 1 and 2 are the zeros of g(x) which are not the zeros f(x) and this happens when a= -2 , b= -2)
Ans: Let the number of questions correctly answered be x
Therefore, number of questions incorrectly answered will be 120 - x.
According to the given condition,
1× x – (1/2)(120-x) = 90
⇒ x - 60 +(1/2)( x = 90
⇒ (3/2) x = 150
Class X Polynomial Test Paper-1