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Let a, b, c be real numbers, a != 0. If ...

Let `a, b, c` be real numbers, `a != 0.` If `alpha` is a zero of `a^2 x^2+bx+c=0, beta` is the zero of `a^2x^2-bx-c=0 and 0 < alpha < beta` then prove that the equation `a^2x^2+2bx+2c=0` has a root `gamma` that always satisfies `alpha < gamma < beta.`

A

`y=(alpha+beta)/(2)`

B

`y = alpha + (beta)/(2)`

C

`y = alpha//2 + beta`

D

`alpha lt y lt beta`

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
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  4. If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are ...

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

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

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

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

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

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

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

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

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

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