Question

To verify graphically that x =2 and x = 5 are the two real zeroes of the quadratic
polynomial x2
‒ 7x + 10.

Answer 1

Answer:

x2 + 7x + 10 = 0

x2 + (5x + 2x) + 10 = 0

x2 + 5x + 2x + 10 = 0

x(x + 5) + 2 (x + 5) = 0

(x + 5) (x + 2) = 0

Hence, zeroes of a given quadratic polynomial are – 5 and – 2.

Sum of zeroes = -2+(-5) = -2-5

= -7/1 = -x coefficient /x² coefficient

Product of zeroes = (-2)(-5)

= 10/1 = constant/x² coefficient

Answer 2

Solution :-

Graph* for this question is given in attachment.

The points where the parabola (curve) cuts the X axis are the roots are the Quadratic equation.

Here, the parabola has cut X axis at points (2, 0) and (5, 0)

So, the roots of the given quadratic equation are 2 and 5.

Let's verify this algebraically.

For this factorise the given polynomial by splitting the middle term.

x² - 7x + 10 = 0

Here, find 2 numbers whose

• Sum is -7 and
• Product is 10

The 2 numbers which satisfies these conditions are -2 and -5

→ x² - 7x + 10 = 0

→ x² - 2x - 5x + 10 = 0

→ x (x - 2) - 5 (x - 2) = 0

→ (x - 5) (x - 2) = 0

So, the zeros are 5 and 2.

★ HENCE VERIFIED ★

*Graph attached is made with Desmos Graph