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Q25. If the polynomials az' +4z +3-4 and z 4+ a leave the same remainder when divided byz 3, find the value of a.t nte is douhle the angle subtended by same chord at |
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Answer» Let f(z) = az³+4z²+3z-4zero of the polynomial (z-3) = 3(since,z-3=0⇒z=3)So,replacing z by 3,f(3) = a(3)³+4(3)²+3(3)-4⇒f(3) = 27a+36+9-4⇒f(3) = 27a+41Let g(z) = z³-4z+azero of the polynomial (z-3) = 3(since,z-3=0⇒z=3)So,replacing z by 3,g(3) = (3)³-4(3)+a⇒g(3) = 27-12+a⇒g(3) = 15+aGiven that the two polynomials leaves same remainder when divided by z-3So,g(3)=f(3)⇒15+a=27a+41⇒15-41 = 27a - a⇒-26 = 26a⇒a=-1. Like my answer if you find it useful! |
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