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614 as and B are the gesels of quader-Fátic polynomial fla): 2-34-2find the polynomial whose gereesCase (22+362 and (32+2B)- Ans: - U2-15w+52) |
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Answer» let alpha= p, bita =qx^2-3x-2p+q= 3pq= -2sum of given zeros= 2p+3q+3p+2q= 5p+5q=5(p+q)= 5×3= 15product of given zeros(2p+3q)(3p+2q)= 6p^2+4pq+9pq+6q^26(p^2+q^2)+13pq= 6{(p+q)^2-2pq}+13(-2)=6{(3)^2-2(-2)}-26=6(9+4)-26=78-26= 52polynomial =x^2-x(sum of given zeros)+product of given zerosx^2-x(15)+(52)x^2-15x+52 let alpha=p and bita = q; p+q =3; pq=-2; sum =2p + 3q +3p + 2q = 5p + 5q =5( p + q) 5(3)=15; product (2p + 3q) (3p + 2q) (2p(3p))+(2p(2q))+3q(3p)+3q(2q)= 6p^2+4qp+9pq+6q^2 = 6(p^2+q^2)-13pq. =6((p+q)^2-2qp)+13(-2) =6((3)^2-2(-2))-26= 6(9+4)-26=6(13)-26=78-26=52; x^2-15x+52=0 |
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