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Statement-1: The cubic equation 4x^(3) -...

Statement-1: The cubic equation `4x^(3) - 15x^(2)+14x-5 = 0` has a root in the internal (2, 3).
Statement-2: If f(x) is a polynomial equation which has two real roots `alpha, beta (alpha lt beta)`, then f(x) = 0 will have a root `gamma such that `alpha lt gamma lt beta`.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statemcnt-2 is True, Statement-2 is Not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

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A DAS GUPTA-Some New Pattern Problems-Exercise
  1. The equations of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3) a...

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  2. Assertion- Reason Type Question:

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  3. Statement-1: The cubic equation 4x^(3) - 15x^(2)+14x-5 = 0 has a root ...

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  4. Consider, L(1) : 2x + 3y + p – 3 = 0 , L(2) : 2x + 3y + p + 3 = 0, whe...

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

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  6. For the following question, choose the correct answer from the codes (...

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  7. Consider three planes P1:x-y+z=1, P2:x+y-z=-1,P3,x-3y+3z=2 Let L1,L2,L...

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  8. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  9. Consider the system of equations ax + by = 0; cx + dy = 0, where a, b,...

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  10. Let f and g be real valued functions defined on interval (-1,\ 1) such...

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  11. Match the integrals in Column I with the values in Column II and indi...

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  12. In the following [x] denotes the greatest integer less than for equal ...

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  13. Match the statement in Column I with the properties in Column II and ...

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  14. Consider the following linear equations ax+ by+cz=0, bx+ cy+az=0, cx+ ...

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  15. Let (x,y) be such that sin-1 (ax) + cos ^-1 (y) + cos ^-1 (bxy)=pi/2...

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  16. Let f(x) =(x^2-6x +5) / (x^2 -5x +6) Match the statement in Column I w...

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  17. Consider the lines give by L1: x+3y -5=0, L2:3x - ky-1=0, L3: 5x +2y ...

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  18. Consider all possible permulations of letter of the word ENDEANOEL.

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  20. Match the statements/expressions given in Column I with the values giv...

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