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solve 0=-1+2x+3x^2...

solve `0=-1+2x+3x^2`

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The correct Answer is:
C
Since `f'(x)=12x^(2)+6x+2`
Here `D=6^(2)-4.12.2=36-96=-60lt0`
`implies` Only one real root for `f(x)=0`
Also `f(0)=1,f(-1)=-2`
`implies` Root must lie in `(-1,0)`
Taking averate of 0 and (-1),f(-1/2)=1/4`
`implies` Root must lie in `(-1,-1/2)`
Similarly `f(-3/4)=-1/2`
`implies` Root must lie in `(-3/4,-1/2)`
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

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  3. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

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  4. solve 0=-1+2x+3x^2

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  5. Find the roots of x^2-6x-2=0

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  6. The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have on...

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  7. The roots of the equation 12 x^2 + x - 1 = 0 is :

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  8. Let for a != a1 != 0 , f(x)=ax^2+bx+c ,g(x)=a1x^2+b1x+c1 and p(x) = f(...

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  9. Sachin and Rahul attempted to solve a quadratic equation. Sachin made ...

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  10. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

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  11. Find the roots of x^2+7x+12=0

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  12. If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:...

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  13. Solve x^2+3x+9=0

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  14. Let alpha and beta be the roots of equation px^(2) + qx + r = 0 , ...

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  15. Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a, then (a) f...

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  16. Solve x^2+4x+4=0

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  17. Let S be the set of all non-zero real numbers such that the quadratic ...

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  18. Find the sum of all real values of X satisfying the equation (x^2-5x+5...

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  19. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

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  20. If, for a positive integer n , the quadratic equation, x(x+1)+(x-1)(x+...

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