3. Find the product of the real roo...
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3. Find the product of the real roots of the equation, x2 + 18x + 30 = 21x2 +18x +45

JEE/Engineering Exams
Maths
Solution
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Let ( x^{2}+18 x+30=z ) ( Rightarrow quad z=2 sqrt{z+15} ) ( Rightarrow quad t^{2}=4(t+15) ) ( Rightarrow quad t^{2}-4 z-60=0 ) ( Rightarrow(t-10)(t+6)=0 ) ( Rightarrow quad t=10,-6 ) ( therefore x^{2}+18 x+30=10 quad ) as ( quad x^{2}+18 x+30=-6 ) ( =5 x^{2}+18 x+20=0 quad ) a ( quad x^{2}+18 x+36=0 ) Pdt ( y times sec t=+20 ) Pat. 9 sorts ( =36 )
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