If ′k′ be the ratio of the roots of the equation x2−px+q=0, the value of 1+k2k is
We know that equation ax2+bx+c=0
Then sum of roots =a−b
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Write the coefficients of x2 in each of the following:(i) 2+x2+x (ii) 2−x2+x3 (iii) 2πx2+x (iv) 2x−1
If α and β are the zeros of the polynomial x2−8x+k such that α2+β2=40, then the value of k is
Verify that −3 is a zero of the polynomial, q(x)=x+3.
Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x)=3x+1,x=−31(ii) p(x)=5x−π,x=54(iii) p(x)=x2−1,x=1,−1(iv) p(x)=(x+1)(x−2),x=−1,2(v) p(x)=x2,x=0(vi) p(x)=lx+m,x=−lm(vii) p(x)=3x2−1,x=−31,32(viii) p(x)=2x+1,x=21
Find all zeroes of the polynomial 2x3+x2−6x−3 if two of its zeroes are −3 & 3
Give examples of polynomials p(x),g(x),q(x) and r(x), which satisfy the division algorithm and(i) deg p(x)=deg q(x) (ii) deg q(x)=deg r(x) (iii) deg r(x)=0
Given that the zeros of the cubic polynomial x3−6x2+3x+10 are of the form a,a+b,a+2b for some real numbers a and b, find the values of a and b
Identify constant, linear, quadratic, cubic polynomial from the following.−z3.