(x^2 - 12 x + 32)÷ (x-8)
(x^2 - 10 x + 21 )÷ (x-7)
Answers
Answer:
(x + 1)2 = 2(x – 3)
=> x2 + 2x + 1 = 2x – 6
=> x2 + 2x + 1 - 2x + 6 = 0
=> x2 + 7 = 0
=> x2 + 0x + 7 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(ii) x2 – 2x = (–2) (3 – x)
=> x2 – 2x = -6 + 2x
=> x2 -2x – 2x + 6 = 0
=> x2 – 4x + 6 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(iii) (x – 2)(x + 1) = (x – 1)(x + 3)
=> x2 – 2x + x – 2 = x2 – x + 3x – 3
=> x2 – x – 2 = x2 + 2x – 3
=> x2 – x – 2 - x2 - 2x + 3 = 0
=> -3x + 1 = 0
=> 3x – 1 = 0
This is not an equation of the form ax2 + bx + c = 0
Hence, the given equation is not a quadratic equation.
(iv) (x – 3)(2x +1) = x(x + 5)
=> 2x2 – 6x + x – 3 = x2 + 5x
=> 2x2 – 5x – 3 = x2 + 5x
=> 2x2 – 5x – 3 - x2 - 5x = 0
=> x2 – 10x – 3 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(v) (2x – 1)(x – 3) = (x + 5)(x – 1)
=> 2x2 – x – 6x + 3 = x2 + 5x – x – 5
=> 2x2 – 7x + 3 = x2 + 4x – 5
=> 2x2 – 7x + 3 - x2 - 4x + 5 = 0
=> x2 – 11x + 8 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.
(vi) x2 + 3x + 1 = (x – 2)2
=> x2 + 3x + 1 = x2 + 4 – 4x
=> x2 + 3x + 1 - x2 - 4 + 4x = 0
=> 7x - 3 = 0
This is not an equation of the form ax2 + bx + c = 0
Hence, the given equation is not a quadratic equation.
(vii) (x + 2)3 = 2x (x2 – 1)
=> x3 + 6x2 + 12x + 8 = 2x3 – 2x
=> x3 + 6x2 + 12x + 8 - 2x3 + 2x = 0
=> -x3 + 6x2 + 14x + 8 = 0
=> x3 - 6x2 - 14x - 8 = 0
This is not an equation of the form ax2 + bx + c = 0
Hence, the given equation is not a quadratic equation.
(viii) x3 – 4x2 – x + 1 = (x – 2)3
=> x3 – 4x2 – x + 1 = x3 - 6x2 + 12x - 8
=> x3 – 4x2 – x + 1 - x3 + 6x2 - 12x + 8 = 0
=> 2x2 – 13x + 9 = 0
This is an equation of the form ax2 + bx + c = 0
Hence, the given equation is a quadratic equation.