Question

rval 1 + 28x + 5, find the value of P(1). TWU U ult Megui. Il P(X) is a factor of both x4 + 6x2 + 25 and Let a, ß, y be distinct real numbers such that aa? + ba + c = (sino)a? +(coso)a aß? + bB + c = (sino)p2 + (coso) ay2 + by + c = (sinO)y2 + (cosO)y (where a, b, c ER) (a) Find the maximum value of the expression 2 a> +6² h 512 (b) If , =aľ + bị+ cả makes an angle with V2 = î+j+VZÊ , then find the number of values of 0 € [0, 2Tc] Did the product of uncommon real roots of the two polynomials P(x) = x4 + 273_8x2_6x +15 and

JEE/Engineering Exams

Maths

Solution

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( C=0, quad Q=sin theta ) ( b=cos theta ) ( operatorname{Nav}_{operatorname{lot}} y=frac{a^{2}+b^{2}}{a^{2}+b^{2}+3 a b+4 b^{2}}=frac{1}{1+4 cos ^{2} theta+3 sin theta cos a} ) Cive rating ( Pleft(2 rightarrow frac{=}{1+2(1+cos 2 theta)+frac{3}{2}} sin 20right. ) Its a quesion in sheet. ( quad=frac{2}{6+4 cos theta+3 sin 2 theta} ) Alen This m max, when demonin ator momin Min of ( 6+3 mathrm{mic}+4 mathrm{cos} mathrm{e} ) ( 6+(pm 5) )