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Quadratic & Other Test 3
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Quadratic & Other Test 3
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  • Question 1/10
    1 / -0

    The least value of 7x + 7-x is _____.

    Solutions

    The minimum value of 7x + 7-x occur at  x = 0

    ∴ 70 + 7o = 1 + 1 = 2.

     

  • Question 2/10
    1 / -0

    If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the value of k must be?

    Solutions

    Roots are real if  D = b2 – 4ac = 0; 36k2 – 144 = 0; k2 = 4, 

     

  • Question 3/10
    1 / -0

    Construct a quadratic equation, whose roots are half of the roots of the equation x2 + 5x + 9 = 0.

    Solutions

    To find a new quadratic equation, whose roots are half of the roots of the equation,

    x2 + 5x + 9 = 0, we have to replace x by 2x.

    ∴ The equation is (2x)2 + 5 (2x) + 9 = 0

    ⇒ 4x2 + 10x + 9 = 0

     

  • Question 4/10
    1 / -0

    A and B are the roots of the equation x2 + bx + c = 0. A2 + B2 = 5 and (A + B)2 = 1.

    What is the value of c?

    Solutions

     Product of root = c/a

    = c (in the given equation)

    (A + B)2 − (A2 + B2) = 2AB

    1 − 5 = 2C (∵ C is product of roots)

    ⇒ −4 = 2C

    ⇒ C = −2

    ∴ Option (b) correct.

     

  • Question 5/10
    1 / -0

    The equation x2 + 4x + k = 0 has real roots. Then.

    Solutions

     

  • Question 6/10
    1 / -0

    Twice of the square of the number is 17 more than the square of two more then the number. Find the sum of the digits of the original number.

    Solutions

    Let the original number be N.

    2N2 = (N + 2)2 + 17

    2N2 = N2 + 4 + 4N + 17

    N2 – 4N – 21= 0

    (N – 7) (N + 3) = 0

    N = 7, So the required sum is 7.

     

  • Question 7/10
    1 / -0

    If x be real. Find the maximum value of 14+ 20x - 10x2.

    Solutions

    Given equation is

    -10x2 + 20x + 14

    a < 0

    ∴ Maximum value will occur at 

    = 24

    ∴ Maximum value of the quadratic equation is 24.

     

  • Question 8/10
    1 / -0

    Mr. David is on tour and he has Rs. 360 for his expenses if he exceeds his tour by 4 days, he must cut down his daily expenses by Rs.3 for how many days is Mr. David out on tour?

    Solutions

     

  • Question 9/10
    1 / -0

    A and B attempt to solve a quadratic equation of the form ax2 + bx + c = 0. A starts with a wrong value of b and gets roots as -3 and -5. B starts with a wrong value of c and gets the roots as 6 and 2. Find the correct roots.

    Solutions

    If A starts with a wrong value of b then equation is

    (x + 3) (x + 5) = 0 [ -3, -5 are roots] 

    ⇒x2 + 5x + 3x + 15 = 0    

     ⇒ x2 + 8x + 15 = 0 -------(i)

    If B starts with a wrong value of c then equation is

    (x – 6) (x – 2) = 0 [ 6, 2 are roots]

    ⇒ x2 – 2x – 6x + 12 = 0

    ⇒ x2 – 8x + 12 = 0 ------(ii)

    Correct quadratic equation is

    x2 – 8x + 15 = 0

    ⇒ x2 – 3x – 5x + 15 = 0

    ⇒ x (x – 3) – 5 (x – 3) = 0

    ⇒ (x – 5) (x – 3) = 0

      So, x = 5 or x = 3.

     

  • Question 10/10
    1 / -0

    If 3x2 + 10x + 8x = 0 has it roots α and β. Find the quadratic equation with roots 1/α and 1/β.

    Solutions

    Equation reciprocal

    ⇒ cx2 + bx + a = 0

    Hence, he require equation = 8x2 + 10x + 3 = 0.

     

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