Maths-
General
Easy

Question

In the xy -plane, the graph of the function f(x)= x squared plus 5 x plus 4  has two x -intercepts. What is the distance between the x-intercepts?

  1. 1
  2. 2
  3. 3
  4. 4

hintHint:

Hint:
  • The (x)-intercept is the point on a graph of a function or equation where it intersects with the (X)-axis

The correct answer is: 3


    Explanation:
    • We have given a quadratic expression f left parenthesis x right parenthesis equals x squared plus 5 x plus 4 .
    • We have to find the distance between the x- intercept .
    • We will first find the points where it cut  x-axis and then find the distance between them
    Step 1 of 1:
    • We have a quadratic expressionf left parenthesis x right parenthesis equals x squared plus 5 x plus 4
    • For finding the points where it cut x-axis , we have to do f(x)=0
    So,
    x squared plus 5 x plus 4 equals 0
    x squared plus 4 x plus x plus 4 equals 0
    x left parenthesis x plus 4 right parenthesis plus 1 left parenthesis x plus 4 right parenthesis equals 0
    left parenthesis x plus 1 right parenthesis left parenthesis x plus 4 right parenthesis equals 0
    Therefore,
    x = - 1
    x = - 4
    Now the distance between them will be
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank row blank row blank row blank end table vertical line minus 4 minus left parenthesis negative 1 right parenthesis vertical line
    vertical line minus 4 plus 1 vertical line
    vertical line minus 3 vertical line
    3
    Hence, Option C is correct.
    .

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