How many solution of equation x^2+y^2=1?
Q.1.How many solution of equation x^2+y^2=1?
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Special question of sum and product of roots
v v Q. (1). If 1,2,3 are the roots of the equation x 3 +ax 2 +bx+c=0 then what is the value of c? Ans. Apply product of roots αβγ= -c/a=- constant term/coefficient of x 3 1x2x3 = -c/1 → 6 = -c → c= - 6 Q.2. If (x+√2) is a factor of kx 2 -√2 x + 1, then what is the value of k? Ans. Putting value of x in given equation so x+ √ 2=0 then x= - √ 2 → k (- √ 2) 2 - √ 2 × (-√ 2) +1 = 0 2k+2+1=0 2k+3=0 → 2k=-3 → k = -3/2 Q.3. What is the factor of the equation (x² -5x) ² -30 (x² -5x) -216=0? Ans. First of all, let x 2 –5x =y then equation become y 2 –30y-216=0 then factorize 216 in two term for example 216=36×6 so, can be written 30y = 36y-6y so y 2 -(36y-6y)-2016=0 y 2 -36y+6y-216=0 taking common we get y(y-36) +6(y-36) =0 so (y-36) (y-6) =0 then y has two values