Question

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Answer 1

10. x²-3x+2x-6

= x(x-3)+2(x-3)

=(x-3)(x+2)

ans 3,-2

others are in the picture

Answer 2

Question :

Write the zeroes of the polynomial x² - x - 6.

Solution :

Factoring and finding the zeroes by splitting the middle term :

• x² - x - 6
• x² - 3x + 2x + 6
• x ( x - 3 ) + 2 ( x - 3 )
• ( x + 2 ) ( x - 3 )
• Zeroes : - 2, 3

The zeroes are -2 and 3.

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Question :

If the sum of the zeroes of the quadratic polynomial kx² - 3x + 5 is 1. Write the value of k.

Solution :

On comparing kx² - 3x + 5 to ax² + bx + c, we get :

• a = k
• b = -3
• c = 5

Sum of the zeroes ( α + β ) = -b/a = 1

• -(-3)/k = 1
• 3 = k

The value of k is 3.

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Question :

If the product of the zeroes of the quadratic polynomial x² - 4x + k is 3. Write the value of k.

Solution :

On comparing x² - 4x + k to ax² + bx + c, we get :

• a = 1
• b = -4
• c = k

Product of the zeroes ( αβ ) = c/a = 3

• c/a = 3
• k/1 = 3
• k = 3

The value of k is 3.

_____________________

Question :

If ( x + a ) is a factor of ( 2x² + 2ax + 5x + 10 ). Find the value of a.

Solution :

• ( x + a ) = 0
• x = -a

Substituting x = -a in 2x² + 2ax + 5x + 10 :

• 2(-a)² + 2a(-a) + 5(-a) + 10 = 0
• 2a² + 2(-a²) - 5a + 10 = 0
• 2a² - 2a² - 5a + 10 = 0
• - 5a + 10 = 0
• a = -10/-5
• a = 2

The value of a is 2.

_____________________

Question :

If ( a - b ), a and ( a + b ) are the zeroes of the polynomial 2x³ - 6x² + 5x - 7, wrote the value of a.

Solution :

On comparing 2x³ - 6x² + 5x - 7 to ax³ + bx² + cx + d, we get :

• a = 2
• b = -6
• c = 5
• d = -7

We know that :

• Sum of the zeroes ( α+ β + γ ) = -b/a
• ( a + b) + a + ( a - b ) = - ( -6 )/2
• a + a + a + b - b = 6/2
• 3a = 3
• a = 3/3
• a = 1

The value of a is 1.