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Exercise 2.2 on page 33 . Hope you like them and do not forget to like , social_share
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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x

(ii) 4s

(iii) 6x

(iv) 4u

(v)t

(vi) 3x

(i) x

= x

= (x - 4) (x + 2)

Therefore, the zeroes of x

(ii) 4s

From (a-b)

= (2s-1)

Therefore, the zeroes of 4s

(iii) 6x

= 6x

= 6x

= (3x + 1) (2x - 3)

Therefore, the zeroes of 6x

(iv) 4u

= 4u

= 4u(u + 2)

Therefore, the zeroes of 4u

(v) t

From (a

= (t - √15) (t + √15)

Therefore, the zeroes of t

(vi) 3x

=3x

= (3x - 4) (x + 1)

Therefore, the zeroes of 3x

S. No |
Sum of zeroes=-(Coefficient of x)/Coefficient of x^{2} |
Product of zeroes= Constant term/Coefficient of x^{2}. |

i) |
4 + (-2) = 2 = -(-2)/1 |
4 × (-2) = -8 = -8/1 |

ii) |
1/2 + 1/2 = 1 = -(-4)/4 |
1/2 × 1/2 = 1/4 |

iii) |
-1/3 + 3/2 = 7/6 = -(-7)/6 |
-1/3 × 3/2 = -1/2 = -3/6 |

iv) |
0 + (-2) = -2 = -(8)/4 |
0 × (-2) = 0 = 0/4 |

v) |
√15 + -√15 = 0 = -0/1 |
(√15) (-√15) = -15 = -15/1 |

vi) |
4/3 + (-1) = 1/3 = -(-1)/3 |
4/3 × (-1) = -4/3 |

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) 1/4, -1

(ii) √2, 1/3

(iii) 0, √5

(iv) 1,1

(v) -1/4 ,1/4

(vi) 4,1

(i) 1/4 , -1 Let the polynomial be ax

p + q = 1/4 = -b/a

pq = -1 = -4/4 = c/a

Now we have two method to find the quadratic polynomial

The polynomial can be written as

k[x

So,

$k[x^2 - (\frac {1}{4})x -1]$

Taking k=4

$4x^2 -x -4$

If we take a= 4, then b = -1, c= -4

Therefore, the quadratic polynomial is 4x

We could choose any of the method to get the polynomial

(ii) √2 , 1/3

Let the polynomial be ax

p + q = √2 = 3√2/3 = -b/a

pq = 1/3 = c/a

If a = 3, then b = -3√2, c = 1

Therefore, the quadratic polynomial is 3x

(iii) 0, √5

Let the polynomial be ax

p + q = 0 = 0/1 = -b/a

pq = √5 = √5/1 = c/a

If a = 1, then b = 0, c = √5

Therefore, the quadratic polynomial is x

(iv) 1, 1

Let the polynomial be ax

p + q = 1 = 1/1 = -b/a

pq = 1 = 1/1 = c/a

If a = 1, then b = -1, c = 1

Therefore, the quadratic polynomial is x

(v) -1/4 ,1/4

Let the polynomial be ax

p + q = -1/4 = -b/a

pq = 1/4 = c/a

If a = 4, then b = 1, c = 1

Therefore, the quadratic polynomial is 4x

(vi) 4,1

Let the polynomial be ax

p + q = 4 = 4/1 = -b/a

pq = 1 = 1/1 = c/a

If a = 1, then b = -4, c = 1

Therefore, the quadratic polynomial is x

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