Maharashtra Board Class 10 Math Part 1 Solution Chapter 2 Practice Set 2.1 – Quadratic Equations
Balbharati Maharashtra Board Class 10 Math Part 1 Solution Chapter 2: Quadratic Equations. Marathi or English Medium Students of Class 10 get here Quadratic Equations full Practice set Solution.
Std |
Maharashtra Class 10 |
Subject | Math Part 1 Solution |
Chapter
Practice set |
Quadratic Equations
2.1 |
Practice Set 2.1
(1) Write any two quadratic equations.
(i) x^{2} + 5x+ 4 = 0
(ii) y^{2} + 9xy + 20 = 0
Are too quadratic equations
(2) Decide which of the following are quadratic equations.
(1) x^{2} + 5x – 2 = 0
Can be represented as ax^{2} + bx + c = 0 form.
∴ It is a quadratic equation.
(2) y^{2} = 5y – 10
Or, y^{2} – 5y + 10 = 0
Can be represented as ax^{2}+ bx + c = 0 form,
∴ It is a quadratic equations
(3) y^{2} + 1/y = 2
Or, y^{2} + 1/y – 2 – 0
Cannot be reported as ax^{2} + bx + c = 0 form
∴ it is not a quadratic equations
(4) x + 1/x = -2
Or, x + 1/x + 2 = 0
Can be represented as ax^{2} + bx + c = 0 form
∴ it is quadratic equation.
(5) (m + 2) (m – 5) = 0
Or, m^{2} – 5m + 2m – 10 = 0
Or, m^{2} – 3m – 10 = 0
Can be represented as ax^{2} + bx + c = 0 form
∴ it is a quadratic equation.
(6) m^{3} + 3m^{2} – 2 = 3m^{3}
Or, m^{3} – 3m^{3} + 3m^{2} – 2 = 0
Or, -2m^{3} + 3m^{2} – 2 = 0
Cannot be represented as ax^{2} + b + c = 0 form.
∴ it is not a quadratic equations
(3) Write the following equations in the form ax^{2} + bx + c = 0, then write the values of a, b, c for each equation.
(1) 2y = 10 – y^{2}
Or, y^{2} + 2y – 10 = 0 is in the form as ax^{2} + bx + c = 0
(2) (x – 1)^{2} = 2x + 3
Or, x^{2} – 2×x×1 + 1^{2} = 2x + 3
Or, x^{2} – 2x – 2x + 1 – 3 = 0
Or, x^{2} – 4x – 2 = 0, in the form of ax^{2} + bx + c = 0
(3) x^{2} + 5x = – (3 – x)
Or, x^{2} + 5x = – 3 + x
Or, x^{2} + 5x – x + 3 = 0
Or, x^{2} + 4x + 3 = 0 is in the form ax^{2} + bx + c = 0
(4) 3m^{2} = 2m^{2} – 9
Or, 3m^{2} – 2m^{2} + 9 = 0
Or, m^{2} + 9 = 0
Or, m^{2} + 0xm + 9 = 0 is in the form a^{2}x^{2} + bx + c = 0
(5) P (3 + 6p) = – 5
Or, 3P + 6p^{2} + 5 = 0
Or, 6P + 3p + 5 = 0 is in the form ax^{2} + b + c = 0
(6) x^{2} – 9 = 13
Or, x^{2} – 9 – 13 = 0
Or, x^{2} – 22 = 0
Or, x^{2} + 0 x – 22 = 0 is in the form ax^{2} + bx + c = 0
(4) Determine whether the values given against each of the quadratic equation are the roots of the equation.
Solution:
(1) x^{2} + 4x – 5 = 0; x = 1, – 1
For x = 1
1^{2} + 4×1 – 5
= 1 + 4 – 5
= 5 – 5
= 0
For x = -1
(-1)^{2} + 4×1 – 5
= 1 – 4 – 5
= -8
≠ 0
∴ x = 1 is a root & x = -1 is not a root
(2) 2m^{2} – 5m = 0, m = 2, 5/2
For m = 2
2×2^{2} – 5×2
= 8 – 10
= – 2
≠ 0
For m = 5/2
2× (5/2)^{2} – 5 × 5/2
= 2 × 25/4 – 25/2
= 0
∴ m = 2 not a root & m = 5/2 is a root.
(5) Find k if x = 3 is a root of equation kx^{2} – 10x + 3 = 0.
Solution:
Given, x = 3 is root of equation kx^{2} – 10x + 3 = 0
∴ Putting x = 3 in equation
k × 3^{2} – 10 × 3 + 3 = 0
Or, 9k – 30 + 3 = 0
Or, 9k = 27
Or, K = 27/9 = 3
(6) One of the roots of equation 5m^{2} + 2m + k = 0 is -7/5. Completely the following activity to find the value of ‘k’.
Solution:
Given, -7/5 is the root 7 quadratic equation.
Put m = -7/5 in the equation
5 × (-7/5)^{2} + 2 × -7/5 + k = 0
Or, 5 × 49/25 – 14/5 + k = 0
Or, 49-74/5 + k = 0
Or, 35/5 + k = 0
Or, k = -7
Here is your solution of Maharashtra Board Class 10 Math Part 1 Solution Chapter 2 Practice Set 2.1 – Quadratic Equations
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