Let f(x) = ax² + bx + c be such that f(1) = 3, f(-2) = $\lambda$  and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then $\lambda$  is equal to:

<p>&nbsp;<math><mrow><mi>f</mi><mrow><mo> (</mo><mrow><mn>0</mn></mrow><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mo>+</mo><mi>λ</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>1</mn><mn>4</mn></mrow></math></p><p><math><mrow><mo>∴</mo><mi>f</mi><mrow><mo> (</mo><mrow><mn>0</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>7</mn><mo>−</mo><mi>λ</mi><mo>=</mo><mi>c</mi></mrow></math></p><p><math><mrow><mi>f</mi><mrow><mo> (</mo><mrow><mn>1</mn></mrow><mo>)</mo></mrow><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>3</mn></mrow></math>&nbsp;……. (i)</p><p><math><mrow><mi>f</mi><mrow><mo> (</mo><mrow><mn>3</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>9</mn><mi>a</mi><mo>+</mo><mn>3</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>4</mn></mrow></math>&nbsp;…… (ii)</p><p><math><mrow><mi>f</mi><mrow><mo> (</mo><mrow><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>4</mn><mi>a</mi><mo>−</mo><mn>2</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mi>λ</mi></mrow></math>&nbsp;…. (iii)</p><p> (ii) – (iii)</p><p><math><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>−</mo><mi>λ</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>, </mo></mrow></math>&nbsp;put in equation (i)</p><p><math><mrow><mn>6</mn><mi>λ</mi><mo>=</mo><mn>2</mn><mn>4</mn><mo></mo><mi>λ</mi><mo>=</mo><mn>4</mn></mrow></math></p>

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