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If |ax^2 + bx+c|<=1 for all x is [0, 1]...

If `|ax^2 + bx+c|<=1` for all x is `[0, 1]`,then

A

`|a|le8`

B

`|b|lgt8`

C

`|c|le1`

D

`|a|+|b|+|c|le17`

Text Solution

Verified by Experts

On putting `x=0,1` and `1/2` we get
`|c|le1`………..i
`|a+b+c|le1`…………ii
and `|a+2b+4c|le4`……….iii
From eqs i,ii and iii we get
`|b|le8` and `|a|le8`
`implies|a|+|v|+|c|le17`
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

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  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

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  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

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  6. If both the roots of the quadratic equation x^2-2kx+k^2+k-5=0 are less...

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  7. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

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  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

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  9. All the values of m for whilch both the roots of the equation x^2-2m x...

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  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

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  11. Let alpha,beta be the roots of the equation x^2-p x+r=0 and alpha/2,2b...

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  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

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  13. Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the ...

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  14. The quadratic equations x^2""6x""+""a""=""0""a n d""x^2""c x""+""6"...

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  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

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  19. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  20. Conder the function f(x)=1+2x+3x^2+4x^3 Let the sum of all distinct ...

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  21. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

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