सरल कीजिए :
(iv) `(2x+p-c)^(2) - (2x- p +c)^(2)`

Simplify: (2x+p-c)^(2)-(2x-p+c)^(2)

Simplify: (2x+p-c)^2-\ (2x-p+c)^2

Find the zero of the polynomial in each of the following cases. (i) p (x) = x+5 (ii) p(x) = x - 5 (iii) p (x) = 2x+5 (iv) p(x) = 3x-2 (v) p(x) =3x (vi) p(x) = ax, a ne 0 (vii) p(x) = cx+d,c ne 0 ,c,d are real numbers

a b clx 22. If abc = P, A = C a band AA' = I if and[b c aonly if a, b, c are the roots of the equation(a) x' +p= 0 (b)x + x = 0(c) x- 2x2 + p = 0 (d) r' +x2 + p = 0

Consider three circles C_(1), C_(2) and C_(3) as given below: C_(1) : x^(2)+y^(2)+2x-2y+p=0 C_(2) : x^(2)+y^(2)-2x+2y-p=0 C_(3) : x^(2)+y^(2)=p^(2) Statement-1: If the circle C_(3) intersects C_(1) orthogonally , then C_(2) does not represent a circle. Statement-2: If the circle C_(3) intersects C_(2) orthogonally, then C_(2) and C_(3) have equal radii.

Consider three circles C_(1), C_(2) and C_(3) as given below: C_(1) : x^(2)+y^(2)+2x-2y+p=0 C_(2) : x^(2)+y^(2)-2x+2y-p=0 C_(3) : x^(2)+y^(2)=p^(2) Statement-1: If the circle C_(3) intersects C_(1) orthogonally , then C_(2) does not represent a circle. Statement-2: If the circle C_(3) intersects C_(2) orthogonally, then C_(2) and C_(3) have equal radii.

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))