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Let f(x) be a quadratic polynomial satis...

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0.
If unity is one root of f(x) = 0 then find the other root.

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To solve the problem, we need to find the other root of the quadratic polynomial \( f(x) \) given that one root is 1 and that \( f(2) + f(4) = 0 \). ### Step-by-Step Solution: 1. **Form the quadratic polynomial**: Since 1 is a root of \( f(x) \), we can express \( f(x) \) in the form: \[ f(x) = a(x - 1)(x - r) ...
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CENGAGE ENGLISH-THEORY OF EQUATIONS-ILLUSTRATION
  1. Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If un...

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  2. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

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  3. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

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  4. Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+...

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  5. Find the remainder when x^2+4x^2-7x+6 is diided by x-1.

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  6. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  7. Let a ne 0 and P(x) be a polynomial of degree greater then 2.If P(x) l...

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  8. Given that x^2+x-6 is a factor of 2x^4+x^3-ax^2+b x+a+b-1, find the va...

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  9. Use the factor theorem to find the value of k for which (a+2b),w h e r...

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  10. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  11. Let f(x)= x^(3) + x + 1 and P(x) be a cubic polynomial such that P(0) ...

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  12. Let f(x) be a polynomial with integral coefficients. If f(1) and f(2)...

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  13. Let a ,b in N and a > 1. Also p is a prime number. If a x^2+b x+c=p f...

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  14. If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the value...

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  15. Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x...

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  16. A certain polynomial P(x)x in R when divided by kx-a ,x-ba n dx-c lea...

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  17. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

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  18. If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/...

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  19. In how many points graph of y=x^3-3x2+5x-3 interest the x-axis?

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  20. Consider the following figure. Answer the following questions (...

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