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If alpha1,alpha2 are the roots of equat...

If `alpha_1,alpha_2` are the roots of equation `x ^2-p x+1=0a n dbeta_1,beta_2` are those of equation `x^2-q x+1=0` and vector `alpha_1 hat i+beta_1 hat j` is parallel to `alpha_2 hat i+beta_2 hat j` , then `p=
a. +-q` b. `p=+-2q` c. `p=2q` d. none of these

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. 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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  3. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

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  4. 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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  5. The integral value of m for which the root of the equation m x^2+(2m-1...

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  6. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

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  7. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real...

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  8. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

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  10. Graph of y = f(x) is as shown in the following figure. Find th...

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  11. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

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  12. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

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  13. If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find it...

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  14. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

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  15. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

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  16. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

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  17. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

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  18. Prove that graphs y=2x-3 and y=x^2-x never intersect.

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  19. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

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  20. If alpha and beta are the rootsof he equations x^2-a x+b=0a n dAn=alph...

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