Advertisements
Advertisements
प्रश्न
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
Advertisements
उत्तर
Let the area of a rectangle be p(x)
p(x) = x2 – 2x – 8
When x + 2 is the side of the rectangle
p(–2) = (–2)2 – 2(–2) – 8
= 4 + 4 – 8
= 8 – 8
= 0
When x – 4 is the side of the rectangle.
P(4) = (4)2 – 2(4) – 8
= 16 – 8 – 8
= 16 – 16
= 0
(x + 2) and (x – 4) are the sides of a rectangle
APPEARS IN
संबंधित प्रश्न
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
Show that (x – 3) is a factor of x3 – 7x2 + 15x – 9. Hence factorise x3 – 7x2 + 15 x – 9
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
