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Priya solved the following quadratic equation by completing the square. Her work is shown.
(+ 6x-11 =0
Original equation
x?+6x=11
Step 1: Isolate the variables to one side
4x +6x+6=17
Step 2: Complete the square when b = 6
(x+3)=17
Step 3: Factor and square the trinomial
x+3=‡/17
Step 4: Take the square root of both sides of the equation
x=-3‡/17
Step 5: Inverse operations to isolate the variable
What mistake did Priya make?
A
In Step 2, Priya did not correctly complete the square.
B
In Step 5, Priya did not finish simplifying her answer.
C
In Step 3, Priya should have also squared the 17.
D
In Step 1, Priya should not have changed the sign of 11

Priya solved the following quadratic equation by completing the square Her work is shown 6x11 0 Original equation x6x11 Step 1 Isolate the variables to one side class=


Answer :

While solving the quadratic equation, in the step 2, Priya did not correctly complete the square.

A quadratic equation is of the form of ax²+bx+c=0.

  • Here x is the variable. a , b and c are constants.
  • A quadratic equation has two solutions.
  • The graph of a quadratic equation is in the form of a parabola.
  • A quadratic equation can be solved in various ways:
  1. Graphical solution
  2. Middle term factorization
  3. completing the square method.

The given quadratic equation is of the form:

x²-6x-11=0

Now solving it by completing the square we get:

or, x²-6x=11  (take all the variable to one side)

or, x²-6x+9=11+9  (complete the square when b=3)

or, (x-3)²=20     (factor and square the polynomial)

or, x = 3 ± √20    (use inverse operations so that the variable is isolated)

Hence Priya made a mistake while completing the square of the equation.

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