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If a, b, c are positive and a = 2b + 3c, then roots of the equation `ax^(2) + bx + c = 0` are real for

A

`|(a)/( c)-11|ge 4 sqrt(7)`

B

`|(c )/(a)-11| ge 4 sqrt(7)`

C

`|(b)/(c )-4 | ge 2 sqrt(7)`

D

`|(c )/(b)-4| ge 2 sqrt(7)`

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A
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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 2
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  2. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0, then prove th...

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  3. If a, b, c are positive and a = 2b + 3c, then roots of the equation ax...

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  4. If a,b,c are positive real numbers, then the number of real roots of t...

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  5. Real roots of the equation x^(2)+5|x|+4=0 are

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  6. The number of real roots of the equation (sin 2^(x)) cos (2^(x))=(1)/(...

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  7. The number of solutions of the equation 5^(x)+5^(-x) =log(10)25, x in ...

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  8. The number of solutions of the equation sin e^(x)=5^(x)+5^(-x) is

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  9. The number of real roots of the equation (x+3)^(4)+(x+5)^(4)=16 is

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  10. The number of real solutions of the equation ((5)/(7))^(2)=-x^(2)+2x-3...

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  11. If a and b (ne 0) are the roots of the quadratic x^(2)+ax+b=0 then the...

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  12. If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

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  13. If a, b, c in R and 2a + 3b + 6c = 0, then the equation ax^(2) + bx + ...

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  14. If (ax^(2)+c) y+(dx^(2)+c')=0 and x is a rational function of y and a...

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  15. If the equation x^(2)-4x+log(1/2)a = 0 does not have two distinct rea...

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  16. Consider the equation of the form x^(2)+ax+b=0. Then number of such eq...

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  17. If alpha,betaare the roots of x^2+px+q=0 and alpha^n,beta^n are the ro...

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  18. If alpha and beta are the ral roots of x ^(2) + px +q =0 and alpha ^(4...

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  19. If alpha, beta, gamma, delta are the roots of the equation x^(4)+4x^(3...

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  20. The number of roots of the quadratic equation 8 sec^(2) theta-6 sec th...

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