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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let P(x) be a polynomial function on R such that P(x)+P(2 x)=5 x^2-18 x R .

Options

  1. Anumber of solutions of P(x)=e^x is 1
  2. Bnumber of solutions of P(x)=e^x is 2
  3. C₀^ d x P(x)+25 = 4
  4. D₀^ d x P(x)+25 = 8

Correct answer

D. ₀^ d x P(x)+25 = 8

Step-by-step solution

Clearly P(x) is quadratic equation. Let P(x)=a x^2+b x+c aligned & a x^2+b x+c+a (4 x^2 )+b(2 x)+c=5 x^2-18 & 5 a=5 a=1 aligned aligned & 3 b=0 b=0 & 2 c=-18 c=-9 aligned P(x)=x^2-9 Now, verify options.

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