Page 19 - mathsvol1ch1to3ans

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(27000 − x) > 500 (27000 − x) < −500

26500 > x (or) 27500 < x

x < 26500 x > 27500

Hence Salary of A is either less than |21000 or more than |33000.

12. Forensic Scientists use h = 61.4 + 2.3F to predict the height h in centimetres for a female whose
thigh bone (femur) measures F cm. If the height of the female lies between 160 to 170 cm, then
find the range of values for the length of the thigh bone?
Not For Sale - Veeraragavan C S veeraa1729@gmail.com
Solution:Given 160 < h < 170
61.4 + 2.3F > 160 61.4 + 2.3F < 170
2.3F > 98.6 (and) 2.3F < 108.6

F > 42.87 F < 47.22

Hence the range of values for the length of the thigh bone is between 42.87cm and 47.22cm.

Exercise - 2.9

1. Construct a quadratic equation with roots 7 and −3.
Solution:Sum of the roots is 4 and product of the roots is −21.
2
Hence the required quadratic equation is x − 4x − 21 = 0.
√
2. A quadratic polynomial has one of its zeros 1 + 5 and it satisfies p(1) = 2. Find the quadratic
polynomial.
Solution: Since the quadratic polynomial has one of its zero in an irrational number, it has roots
√
√
1 + 5, 1 − 5 also will be the roots. Sum of the roots is 2 and product is −4. Hence the
2
quadratic polynomial is x −2x−4 = 0. Now p(1) = 2. Hence the quadratic polynomial becomes

2
2
− (x − 2x − 4) = 0
5 √
2
3. If α and β are the roots of the quadratic equation x + 2x + 3 = 0, form a quadratic polynomial
1 1
with zeroes , .
α β
Solution: √
Sum of the roots = α + β = − 2
Product of the roots = αβ = 3
√
1 1 α + β 2
SUM + = = −
α β αβ 3
1 1
PRODUCT =
αβ √ 3
2
The quadratic polynomial is 3x + 2x + 1 = 0
2
4. If one root of k(x − 1) = 5x − 7 is double the other root, show that k = 2 or −25.
Solution:Let the roots be α and 2α.