Question

Question 1- explain how Sheldon immediately knew howard was incorrect?

Answer 1

Answer:

Part 1) In the procedure

Part 2) In the procedure

Step-by-step explanation:

Part 1) Observing the graph

The roots are x=-1/2 and x=4

Remember that, the roots are the x-values when the value of y is equal to zero (the x-intercepts)

That's why Sheldon immediately realizes Howard's solution is incorrect

Part 2) we have

$y=2x^{2}-7x-4$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

equate the equation to zero

$2x^{2}-7x-4=0$  

so

$a=2\\b=-7\\c=-4$

substitute

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(2)(-4)}} {2(2)}$

$x=\frac{7(+/-)\sqrt{49+32}} {4}$

Howard's error is in this step, is wrong with the sign of the number 7, is positive instead of negative

$x=\frac{7(+/-)\sqrt{81}}{4}$

$x=\frac{7(+/-)9}{4}$

$x=\frac{7(+)9}{4}=4$

$x=\frac{7(-)9}{4}=-1/2$