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Given alphaa n dbeta are the roots of t...

Given `alphaa n dbeta` are the roots of the quadratic equation `x^2-4x+k=0(k!=0)dot` If `alphabeta,alphabeta^2+alpha^2beta,alpha^3+beta^3` are in geometric progression, then the value of `7k//2` equals__________.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8...

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  2. If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negati...

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  3. Given alphaa n dbeta are the roots of the quadratic equation x^2-4x+k...

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  4. If (x^2+a x+3)/(x^2+x+a) takes all real values for possible real value...

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  5. If cos^4theta+alpha and sin^4theta+alpha are the roots of the equation...

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  6. If the roots of the equation x^2+a x+b=0 are c and d , then roots of ...

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  7. If a ,b ,c in R a n d a b c<0 , then equation b c x^2+(2b+c-a)x+a...

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  8. For the quadratic equation x^2+2(a+1)x+9a-5=0, which of the following ...

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  9. Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor ...

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  10. If |a x^2+b x+c|lt=1 for all x in [0, 1], then a.|a|lt=8 b. |b|>8 ...

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  11. Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c<0...

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  12. If roots of a x^2+b x+c=0 are alphaa n dbetaa n d4a+2b+c >0,4a -2b+c >...

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  13. The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has

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  14. Find the complete set of values of a such that (x^2-x)/(1-a x) atta...

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  15. If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots o...

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  16. If he roots of the equation12 x^2-m x+5=0 are in the ratio 2:3 then fi...

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  17. Ifalpha,beta be the roots of x^2-a(x-1)+b=0,then the value of 1/(alpha...

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  18. The equation formed by decreasing each root of ax^(2)+bx+c=0 by 1 is2x...

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  19. If the sum of the roots of an equation is 2 and the sum of their cubes...

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  20. If x is real and (x^2+2x+c)/(x^2+4x+3c) can take all real values, of t...

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