Quadratic Equation : CBSE (X) - RDS:8.1
Determine whether the given values are solution of the given equation or not. x² + x + 1 = 0, x = 0, x = 1
x = 0 is NOT a solution (0)² + 0 + 1 = 1 ≠ 0 x = 1 is NOT a solution (1)²+ 1 + 1 = 1 + 1 + 1 = 3 ≠ 0
Determine whether the given values are solution of the given equation or not. x² - 3x + 2 = 0, x = 2, x = -1
x = 2 is a solution (2)² -3(2) + 2 = 4 - 6 + 2 = 0 x = -1 is NOT a solution (-1)² - 3(-1) + 2 = 1 + 3 + 2 = 6 ≠ 0
Determine whether the given values are solution of the given equation or not. a²x² - 3abx + 2b² = 0, x = a/b, x=b/a
x = a/bis NOT a solution a²(a/b)² -3ab(a/b) + 2b² = a⁴/b² - 3a² + 2b² ≠ 0 x = b/a is a solution a²(b/a)² - 3ab(b/a) + 2b² = b² - 3b² + 2b² = 0
Determine whether the given values are solution of the given equation or not. x² - 3√3x + 6 = 0, x = √3, x = -2√3
x = √3 is a solution (√3)² - 3√3(√3) + 6 = 3 -9 +6 = 0 x = -2√3 is NOT a solution (-2√3)² -3√3(-2√3) + 6 = 12 + 18 + 6 = 36 ≠ 0
Determine whether the given values are solution of the given equation or not. x + 1/x = 13/6, x = 5/6, x = 4/3
x = 5/6 is NOT a solution (5/6) + 1/(5/6) = 5/6 +6/5 = 61/30 ≠ 13/6 x = 4/3 is NOT a solution (4/3) + 1(4/3) = 4/3 + 3/4 =25/16 ≠ 13/6
Find the value of 'k' for which the given value is a solution of the given equation x² + 3ax + k = 0, x = -a
(-a)² + 3a(-a) + k =0 a² - 3a² + k =0 -2a² + k = 0 k = 2a²
Find the value of 'k' for which the given value is a solution of the given equation x² - x(a+b) + k = 0, x = a
(a)² - (a+b)(a) + k = 0 a² - a² - ab + k = 0 -ab + k = 0 k = ab
Find the value of 'k' for which the given value is a solution of the given equation 7x² + kx - 3 = 0, x = 2/3
7(2/3)² + k(2/3) - 3 = 0 28/9 + k(2/3) - 3 = 0 1/9 + k(2/3) = 0 k = (-1/9)/(2/3) = - 1/6
Is the following a Quadratic equation? x + 1/x = x², x ≠ 0
No Multiplying by x the equation becomes x² + 1 = x³
Is the following a Quadratic equation? x - 3/x = x²
No Multiplying by x, the equation becomes x² - 3 = x³. The degree is 3
Is the following a Quadratic equation? x²+ 1/x² = 5
No Multiplying by x², the equation becomes x⁴ + 1 = 5x². The degree is 4
Is the following a Quadratic equation? (2x + 1) (3x + 2) = 6(x-1)(x-2)
No On simplifying the equation becomes 6x² + 7x + 2 = 6x² - 18x +12 7x + 2 = -18x + 12
Is the following a Quadratic equation? x(x + 1) + 8 = (x+2)(x-2)
No On simplifying the equation becomes x² + x + 8 = x² - 4 x + 12 = 0
Is the following a Quadratic equation? (x + 1/x)² = 3(x + 1/x) + 4
No On simplifying the equation will become x² + 1/x² + 2 =3x + 3/x + 4 x² - 3x -3/x + 1/x² + 2 = 0
Is the following a Quadratic equation? 2x² - 3√x + 9 =0
No The given equation does not have a quadratic polynomial It has fractional power.
Is the following a Quadratic equation? x² -2x - √x - 5 = 0
No The given equation does not have a quadratic polynomial It has fractional power..
If x=2/3 and x=-3 are roots of the equation ax²+7x+b=0, find the value of a and b.
Since x=2/3 is a root a(2/3)² + 7(2/3) + b = 0 4a/9 + 14/3 + b = 0 multiplying by 9 4a + 42 + 9b = 0 4a + 9b = -42 --------> (1) Since x = -3 is a root, we will get 9a + b = 21 --------->(2) Solving (1) and (2), we get a=3 and b=-6
Determine whether the given values are solution of the given equation or not. 2x² - x + 9 = x² + 4x +3, x = 2, x = 3
The equation can be simplified as x² - 5x + 6 = 0 x = 2 is a solution (2)² - 5(2) + 6 = 4 -10 + 6 = 0 x = 3 is a solution (3)² = 5(3) + 6 = 9 -15 +6 = 0
Is the following a Quadratic equation? x² + 6x - 4 = 0
Yes
Is the following a Quadratic equation? √3x² -2x +½ = 0
Yes
Is the following a Quadratic equation? x² - 3x = 0
Yes Here the constant term (c) is zero, but the polynomial expression is quadratic.
Is the following a Quadratic equation? x + 1/x = 1
Yes Multiplying by x, the equation becomes x² + 1 = x
Is the following a Quadratic equation? 16x² - 3 = (2x + 5) (5x - 3)
Yes On simplifying the equation becomes 16x² - 3 = 10x² - 19x -15 6x² + 19x + 12 = 0
Is the following a Quadratic equation? (x + 2)³ = x³ - 4
Yes On simplifying the equation becomes x³ + 6x² + 12x + 8 = x³ -4 6x² + 12x + 12 = 0
Is the following a Quadratic equation? 3x² - 5x + 9 = x² - 7x + 3
Yes On simplifying the equation will become 2x² + 2x + 6 = 0
Find the value of 'k' for which the given value is a solution of the given equation kx² +√2x - 4 = 0, x=√2
k(√2)² +√2(√2) - 4 = 0 2k +2 - 4 =0 2k = 2 k = 1
Determine, if 3 is root of equation given below (x² -4x + 3)^½ +(x² - 9)^½ = (4x² - 14x +16)^½
putting x=3 in the equation LHS = (9 - 12 +3)^½ + (9-9)^½ = 0 RHS = (36 - 42 + 16) = 10 LHS ≠ RHS x = 3 is NOT a solution to the given equation
Determine whether the given values are solution of the given equation or not. x² - √2x - 4 = 0, x = -√2, x = -2√2
x = -√2 is a solution (-√2)² - √2(-√2) - 4 = 2 + 2 - 4 = 0 x =-2√2 is NOT a solution (-2√2)² - √2(-2√2) - 4 = 8 + 8 - 4 = -12 ≠ 0