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If the equation `(a-5)x^2+2(a-10)x+a+10=0` has roots of opposite sign, then find the value of `adot`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the root...

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  2. If the fraction (x^3+(a-10)x^2-x+a-6)/(x^3+(a-6)x^2-x+a-10) reduces to...

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  3. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

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  4. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

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  5. If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alp...

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  6. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

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  7. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval i...

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  8. The values of 'a' for which 4^x-(a-4) 2^x+(9a)/4<0 AAx in(1,2) is

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  9. Find the number of positive integral values of k for which kx ^(2) +(k...

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  10. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

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  11. Given that a ,b ,c are distinct real numbers such that expressions a ...

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  12. Find the number of quadratic equations, which are unchanged by squarin...

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  13. Solve the following: (sqrt(x^2-5x+6)+sqrt(x^2-5x+4))^(x/2)+(sqrt(x^2-...

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  14. Show that the equation A^2//(x-a)+B^2//(x-b)+C^2//(x-c)+...+H^2//(x-h)...

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  15. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

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  16. If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of th...

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  17. If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic...

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  18. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

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  19. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

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  20. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

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