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2. Find the value of discriminant.

    (1) \(x^2\) + 7\(x \) – 1 = 0

    (2) 2\(y^2\) – 5y + 10 = 0

    (3) \( \sqrt{2} x^2\) + 4\(x \) +  \(2\sqrt{2} \)= 0

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(1)    \(x^2\) + 7\(x \) – 1 = 0

Sol.  \(x^2\) + 7\(x \) – 1 = 0
       Comparing with  a\(x^2\) + b\(x \) + c =  0
       we get, a = 1, b = 7 and c = –1
∴    \(b^2\) – 4ac  = \(7^2\) – 4 × 1 × –1
∴               Δ  =  49  +  4
∴               Δ  =  53
The value of discriminant is 53.

 

 (2)   2\(y^2\) – 5y + 10 = 0


Sol.  2\(y^2\) – 5y + 10 = 0
        Comparing with  a\(x^2\) + b\(x \) + c =  0
        we get, a = 2, b = –5 and c = 10
∴     
\(b^2\) – 4ac  = \({(-5)^2}\) – 4 × 2 × 10
∴                Δ   =  25 – 80
∴                Δ   =  –55
The value of discriminant is –55.

 

(3)   \( \sqrt{2} x^2\) + 4\(x \) +  \(2\sqrt{2} \)= 0

Sol.   \( \sqrt{2} x^2\) + 4\(x \) +  \(2\sqrt{2} \)= 0  comparing
        with  a\(x^2\) + b\(x \) + c =  0
        We get, a = \( \sqrt2\)  b = 4 and c = \(2\sqrt{2} \)
∴        \(b^2\) – 4ac  =  \(4^2\) – 4 ×\( \sqrt2\) × \(2\sqrt{2} \)
∴                 Δ   =  16 – 16
∴                 Δ   =   0
∴    The value of discriminant is 0.

uÉaÉïxÉqÉÏMüUhÉ August 10 , 2018 0 Comments 12 views