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How many real solutions does the equatio...

How many real solutions does the equation `x^7+14 x^5+16 x^3+30 x-560=0` have?

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To determine how many real solutions the equation \( x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 \) has, we will analyze the function and its derivative. ### Step 1: Define the function Let \[ f(x) = x^7 + 14x^5 + 16x^3 + 30x - 560 \] ...
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CENGAGE ENGLISH-THEORY OF EQUATIONS-ILLUSTRATION
  1. Sketch the graph of the following functions y=f(x) and find the numbe...

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  2. Find how many roots of the equations x^4+2x^2-8x+3=0.

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  3. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  4. Solve sqrt(5x^(2) - 6x + 8) + sqrt(5x^(2) - 6x - 7) = 1

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  5. Solve (x^2-5x+7)-(x-2)(x-3)=1.

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  6. Solve the equation 4^(x)- 5 xx2^(x) + 4 = 0.

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  7. Solve the equation 12^x-56 x^2+89 x^2-56 x+12=0.

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  8. Solve the equation 3x^(2-x)+4x^2=25.

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  9. Solve the equation (x-1)^4+(x-5)^4=82.

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  10. Solve the equation (x+2)(x+3)(x+8)xx(x+12)=4x^2dot

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  11. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

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  12. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

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  13. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

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  14. If roots of equation x^3-2c x+a b=0 are real and unequal, then prove t...

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  15. Find the quadratic equation with rational coefficients whose one root ...

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  16. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac!=0, then prove that f...

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  17. If a ,b ,c(a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 ares rational.

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  18. If a gt 0 and b^(2) - 4 ac = 0 then solve ax^(3) + (a + b) x^(2) + (b ...

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  19. If a ,b ,a n dc are odd integers, then prove that roots of a x^2+b x+c...

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  20. If aa n dc are odd prime numbers and a x 62+b x+c=0 has rational roots...

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