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If alphaa n dbeta are the roots of x^2+p...

If `alphaa n dbeta` are the roots of `x^2+p x+q=0a n dalpha^4,beta^4` are the roots of `x^2-r x+s=0` , then the equation `x^2-4q x+2q^2-r=0` has always. one positive and one negative root two positive roots two negative roots cannot say anything

A

two real roots

B

two negative roots

C

two positive roots

D

one positive and one negative roots

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

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  2. Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...

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  3. If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are ...

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  4. The equation (cosp-1)^x^2+(cos p)x+s in p=0 in the variable x has real...

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  5. The number of real solution of the equation. sin(e^(x))=5^(x)+5^(-x) ...

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  6. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

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  7. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  8. Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to ...

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  9. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

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  10. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

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  11. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

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  12. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

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  13. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  14. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

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  15. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

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  16. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  17. Fill in the blanks If the quadratic equations x^2+a x+b=0a n dx^2+b x+...

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  18. Find the values of a for which the roots of the equation x^2+a^2=8x+6a...

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  19. If the sum of the roots of the equation (a+1)x^2=(2a+3)x+(3a+4)=0 is -...

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  20. If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciproca...

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