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Determine the nature of the roots of the...

Determine the nature of the roots of the following equatins :
(a) `x^(3) + 2x +4 = 0`
(b) `3x^(2) - 10x + 3 = 0`
(c ) `x^(2) - 24x + 144 = 0`

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Verified by Experts

The correct Answer is:
(a) Complex conjugates
(b) Real and distinct
(c ) Real equal
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PEARSON IIT JEE FOUNDATION-QUADRATIC EXPRESSIONS AND EQUATIONS-Short Ans
  1. Factorize the following quadratic expressions : (a) x^(2) + 5x + 6 ...

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  2. Determine the nature of the roots of the following equatins : (a) x^...

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  3. If f(x) = x^(2) - 5x -36 and g(x) = x^(2) + 9x + 20, then for what va...

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  4. solve : 16x^(4)- 28x^(2) - 8 = 0

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  5. For what values of m does the equation, mx^(2) + (3x-1)m + 2x + 5 = 0 ...

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  6. Find the value of m for which the quadratic equation , 3x^(2) + 10x + ...

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  7. If a, b are the roots of the equation x^(2) - px +q = 0, then find the...

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  8. If one roots of the equation x^(2) - mx + n = 0 is twice the other roo...

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  9. The square of one-sixth of the number of students in a class are stud...

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  10. If 2alpha and 3beta are the roots of the equation x^(2) + az +b = 0, t...

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  11. If alpha, beta are the roots of the quadratic equation lx^(2) + mx + n...

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  12. By a reduction of re.-1 per kg in the price of sugar Mohan can buy one...

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  13. The zeroes of the quadratic polynomial x^(2) - 24x + 143 are

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  14. Find the quadratic equation in x whose roots are (-7)/(2) and (8)/(3).

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  15. If k(1) and k(2) are roots of x^(2) - 5x - 24 = 0, then find the quad...

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  16. The product of the roots of the equation 1/(x+1) + (1)/(x-2) = (1)/...

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  17. The roots of the equation 2x^(2) + 3x + c = 0 (where x lt 0) could be ...

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  18. The roots of the equation 3x^(2) - 4sqrt(3x) + 4 = 0 are

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  19. If alpha and beta are the roots of the quadratic equation x^(2) + 3x -...

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  20. The roots of the equtation (x-3)/(x-2) + (2x)/(x+3) = 1, where x ne 2,...

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