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Find the roots of each of the following ...

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

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Verified by Experts

The correct Answer is:
`x=(2a+b)" or "x=(2a-b)`
`x^(2)-4ax+(2a+b)(2a-b)=0`
`impliesx^(2)-(2a+b)x-(2a-b)x+(2a+b)(2a-b)=0`
`impliesx{x-(2a+b)}-(2a-b){x-(2a+b)}=0`
`implies{x-(2a+b)}{x-(2a-b)}=0`
`impliesx=(2a+b)" or "x=(2a-b).`
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RS AGGARWAL-QUADRATIC EQUATIONS -Test Yourself
  1. The roots of the quadratic equation 2x^2 - x - 6 = 0 are

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  2. Find the discriminant of the quadratic equation 3sqrt3x^2+10x+sqrt3=0.

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  3. If the roots of the quadratic equation 2x^(2)+8x+k=0 are equal, find t...

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  4. If the quadratic equation p x^2 - 2 sqrt(5)px + 15 = 0 has two equal ...

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  5. If 1 is a root of the equation ay^(2)+ay+3=0" and "y^(2)+y+b=0 then fi...

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  6. If one zero of the polynomial x^3-4x+1 is 2+sqrt3 write the other zero

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  7. If one root of the quadratic equation 3x^(2)-10x+k=0 is reciprocal of ...

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  8. Find the value of p for which the roots of the equation px (x — 2) + 6...

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  9. Find the value(s) of k so that, the quadratic equation x^2 - 4kx + k =...

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  10. Find the nonzero value of k for which the roots of the quadratic equat...

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  11. Solve: x^2-(sqrt3+1)x+sqrt3 = 0

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  12. Solve: 2x^2+a x-a^2=0

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  13. Find the roots of the following quadratic equations by the factorisati...

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  14. Solve : sqrt(3)x^(2)+10x-8sqrt(3)=0.

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  15. Solve for x sqrt3x^2-2sqrt(2)x-2sqrt3=0

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  16. Solve by factorization: 4sqrt(3)x^2+5x-2sqrt(3)=0

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  17. Solve by factorization: 4x^2+4b x-(a^2-b^2)=0

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  18. Solve x^(2)+5x-(a^(2)+a-6)=0.

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  19. Solve for x: x^2+6x-(a^2+2a-8)=0

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  20. Find the roots of each of the following equations, if they exist, by a...

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